So i was looking through tasha's cauldron of everything and thought about an orc Rune knight. Then I thought that if I add a class into Barbarian I could do some real damage. My question, is can you use the Giant's Might Feature from Rune Knight and Rage?

Seems like it would work. You can’t cast while raging, but giant’s might isn’t a spell and doesn’t require concentration.
Most important would be to confirm it with your DM.  Their opinion will matter more than anyone on here. 

Have you tried playing this since posting? I am creating a Rune Knight Tortle with the intention of multiclassing into barbarian, and I'm curious about other people's experiences. 

I actually used it as an npc against my players and they have a hard time fighting him. Really satisfying.

It may not be all that useful to ask someone who posted over a year ago how things came out.

If a Barbarian can use Giant's Might at all while raging might be a DM call, but if they use it before they rage, that's fine, and all it does is let them be a large creature (this has no game effects aside from the fact that if there isn't room for a large creature they can't use the ability at all) and the gain the ability to use an Unarmed Strike or an Attack with a Weapon that does an extra 1d6 damage (this effect gains no benefit from Strength) once per turn.

A Tortle has Natural Armor, which might not in any way interact with Unarmored Defense.  They ought not stack, so a Tortle player character would get to chose if they get an armor class of 17 which cannot be adjusted by Dexterity, and with a Shield would give them a 19, or Unarmored Defense, which gives them a base Armor class of 10, plus their Dex and Con bonus and another plus 2 with a shield.

Given that is it not entirely clear how Unarmored Defense and Natural Armor interact, just like Xalthu said in the second post, ask your DM.

It has been discussed at length that unarmored Defense and Natural Armor don't stack. The same goes for Stuff like mage armor or normal armor. You can only use one AC calculation at once.

That said I don't see why Rune Knight and Barbarians features couldn't both be active at the same time. If you use giant might you can still use rage and vice versa. Problem would be that you'd neet two rounds to set it up, by which point a lot of fights are already decided.

Quote from Geann>>

all it does is let them be a large creature (this has no game effects)

Being Large has a number of differences on its own:

• You occupy a 10x10 foot space (rather than the normal 5x5). This is both a benefit and penalty as it means you can reach more targets, but more can reach you. You're more easily hit by area effects, but you can also block a typical corridor on your own, enemies have further to move around you (to avoid attacks of opportunity) and so-on.
• You can carry, lift and drag twice as much weight.
• You can grapple and shove Huge creatures and conversely cannot be grappled or shoved by anything smaller than Medium. This also applies to a number of other abilities and effects that specify a size class restriction (usually they say "no more than one size larger" or similar).
• Medium creatures can potentially use you as a mount (up to your DM).
• You will find it harder to benefit from cover (half cover for a Medium creature will probably only protect your shins and so-on), however you could provide cover for Medium and smaller creatures if you want to protect them.
• You are eight times heavier (doubled in size in three dimensions). Another mixed benefit as you could absolutely flatten someone by landing on them, but good luck climbing up that balsa wood ladder!

I feel like I'm missing a couple bullet points; there's some stuff about the amount of food and water you need but it won't matter for a temporary effect.

Given that is it not entirely clear how Unarmored Defense and Natural Armor interact, just like Xalthu said in the second post, ask your DM.

Actually the rules clarify this point:

Some spells and class features give you a different way to calculate your AC. If you have multiple features that give you different ways to calculate your AC, you choose which one to use.

A Tortle's Natural Armor and a Barbarian's Unarmored Defense are both different ways to calculate your AC, so you have to pick which one to use. Can't imagine why you'd ever pick the worse one though, so I'd assume you just use Natural Armor until your Unarmed Defense is higher, but growing Unarmed Defense means putting points in DEX in addition to STR and CON so you may not actually reach that point.

Quote from Haravikk >>

You are eight times heavier (doubled in size in three dimensions). Another mixed benefit as you could absolutely flatten someone by landing on them, but good luck climbing up that balsa wood ladder!

 not to be that guy, but that isn't anywhere in the rules. RAW you don't get heavy from Giants Might as opposed by getting bigger through the enlarge spell (which does say that you get heavy). You could argue that you just blow up like a balloon. I wouldn't go for that interpretation though, since it would make the fighter float like a rubber duck. 

Quote from Sutlo >>

Quote from Haravikk >>

You are eight times heavier (doubled in size in three dimensions). Another mixed benefit as you could absolutely flatten someone by landing on them, but good luck climbing up that balsa wood ladder!

 not to be that guy, but that isn't anywhere in the rules. RAW you don't get heavy from Giants Might as opposed by getting bigger through the enlarge spell (which does say that you get heavy). You could argue that you just blow up like a balloon. I wouldn't go for that interpretation though, since it would make the fighter float like a rubber duck. 

That's my bad, I could have sworn it was included in the Giant's Might text (as with Enlarge/Reduce), maybe it was in the UA? Doesn't matter, I'll score that part out in my post. Thanks for the correction!

I think it's because it sets the size to large if you're smaller than large. Since it isn't clear what size category the character was before, they would have to use some elaborate speech to make wieght changes happen, which they probably didn't want to do for something that won't ever come up in most games and can be decided by a DM pretty easy.

Of course that "setting" of the size category makes for some wonky at least interactions (cast reduce on a small sized character, then the small character uses giants might/runic juggernaught to go to huge size. If you're using the weight and volume calculations from enlarge/reduce but don't change the weight, the character would now grow its volume by 8*8*8*8 = 4096 and then have a density lighter than air.

Quote from Sutlo >>

I think it's because it sets the size to large if you're smaller than large. Since it isn't clear what size category the character was before, they would have to use some elaborate speech to make wieght changes happen, which they probably didn't want to do for something that won't ever come up in most games and can be decided by a DM pretty easy.

Of course that "setting" of the size category makes for some wonky at least interactions (cast reduce on a small sized character, then the small character uses giants might/runic juggernaught to go to huge size. If you're using the weight and volume calculations from enlarge/reduce but don't change the weight, the character would now grow its volume by 8*8*8*8 = 4096 and then have a density lighter than air.

Yeah, it's a bit strange it wasn't just a copy/paste of the enlarge part of Enlarge/Reduce (with a smaller damage dice); I half expected them to just make it a free casting of Enlarge/Reduce for the simplicity, and to eliminate the combo of Giant's Might + Enlarge/Reduce to become Huge dealing d6+d4 extra damage per hit, or at least add "and effects to change your size further will fail" or such. Though on the other hand, being able to have a Halfling Fighter go from Small to Huge in two steps is pretty amusing.