I am new to dnd and I was coming up with a new character for a campaign some friends and I might run. I want it to be a wizard that has "taken a vow of silence". When in reality he was cursed and the curse doesn't allow him to talk to anyone about the curse and switched his body with his familiar. The wizards main goal is to get the wish spell to reverse the curse so he can be in his normal body. Would this be possible? The main thing I don't know about is if the wizard, technically the familiar, how would it summon the "familiar" that's actually the wizard. Sorry if this seems like a stupid idea. I'm still very new to role playing games in general and this is about 5e if that helps or changes things. 

While I don't think this is a stupid idea, it is a difficult one to make work. You need to be able to speak as a spellcaster. Here's what I suggest:

Start as a Warlock and play up to 2nd level. Decide to become a Wizard(level 1) for more power, your jealous Patron steps in and punishes you by the Curse, trying to force you back on their path but, not removing all your power. Level to 3rd in Warlock and take Pact of the Chain and the Voice of the Chain Master Invocation. If your bodies are switched, this should allow you to speak through your original body. Your Patron, amused by your strength of will, watches how things will play out. You go back to leveling in Wizard and play out your character concept.

Problems: No fake vow of silence.  You have dangerously low HP in a Familiar's body. Your stats for all abilities would(could) go off of your Familiar's. Probably many other things I haven't thought of. 

Thank you for your advice! I may do that but I may not do it just because it seems like too much trouble. I was just brainstorming weird ideas with a friend and this came up.

If you are still considering this as an option, I think the solution might be one closer to a daft idea I had for a character a while back which was:

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Character Name: Frumplestiltskin (combination of Rumpelstiltskin and Frumpkin from Cit Role), Race Tabaxi, Class: Shadow or Wild magic Sorcerer

Why is it daft? well.....Frumplestiltskin died and a was reincarnated by a druid, it was the druids first ever attempt at a Reincarnation spell and the first time he had seen a Tabaxi and the spell went a little...wrong...Frumplestiltskin came back as a Cat, a normal house hold cat. He still has all the same ability scores, spells etc he just has the size and appearance of a cat. This will cause some issues with acquiring magical items but the gem he used as an arcane focus will certainly spiff up his collar.

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So adapting that to your idea, you could have it that the wizard died and got a cursed reincarnation where his soul went into the body of his familiar. His real body is being kept somewhere in a suspended animation type affair (in the style of the Magic Jar spell) and so the wizard wanders the material plane trying to get enough power to undo the curse.

Everything from a game mechanic stand point stays the same, you keep all your hit points, proficiencies etc as if you were a normal human (or whatever race you planned)  wizard its just you size and form is that of your familiar but with the slight adjustment of having enough manual dexterity and the ability speak to cast spells, i'd say for ability scores roll or use the standard array or point buy as normal then, keep you Int, Wis and Cha scores but your Str, Dex and Cons becomes that of the familiar. Just bear in mind you will have a vastly lower carrying capacity and any equipment/armour will need to be custom made and you'll likely need to come to an arrangment with other characters about carrying any material components for your spells and your spell book.

Quote from Turtlehumps >>

I am new to dnd and I was coming up with a new character for a campaign some friends and I might run. I want it to be a wizard that has "taken a vow of silence". When in reality he was cursed and the curse doesn't allow him to talk to anyone about the curse and switched his body with his familiar. The wizards main goal is to get the wish spell to reverse the curse so he can be in his normal body. Would this be possible? The main thing I don't know about is if the wizard, technically the familiar, how would it summon the "familiar" that's actually the wizard. Sorry if this seems like a stupid idea. I'm still very new to role playing games in general and this is about 5e if that helps or changes things. 

 
Might make more sense to get the Remove Curse spell. Getting to 5th level for Remove Curse is certainly easier than getting to 17th level for Wish.

Also note: you cannot provide Somatic components in the body of an animal since they are complicated hand gestures. Being unable to speak means being unable to provide Verbal components, which are magic words. So, basically, you'll be unable to cast any spells. Ever. Not a very effective wizard.

My advice? Don't do this. The complications of a wizard that can't provide S or V components, the swapping of bodies with familiar and how that involves the dismissing action, and so on, are nothing but headaches for a DM to factor and keep balance. You'll be a party member that cannot attack and cannot cast spells, cannot communicate and basically a pointless addition to the party. Trying to create encounters where your character's presence isn't going to severely hinder everything the party is trying to do is going to be a constant chore for the DM. Or the DM has to invent and change rules to let you stay effective but without breaking the balance. That's going to be difficult.

It's not a stupid idea, as I can see where the idea of something different comes from but it's an idea made without an understanding of D&D 5Es rules and without realising what it would involve the DM having to do. It's not stupid, just very impractical.

Thank you for your advice. I don't plan to do this anymore. I don't wanna cause problems for the DM and it just seems like it's definitely not worth it.