Sorcerer blood problem

One of my players is playing a warforged sorcerer draconian bloodline but as they are built they don’t have blood. One of my quests for my players is a background quest about them so to maybe explain how they got magic although I’m not sure how to do it. 

Draconic Bloodline is a broad statement to say that the magic they wield comes from a link to the natural magic of the dragons.

Maybe make it that the core of every warforged is a precious metal magical heart, which imbues the warforged with the energy to animate. It doesn't beat or pump blood, but in this case, the gold of the heart came from a dragons horde - that's where the magic came from.

As for the quest - the dragon wants it back. Or, it is part of a pair of items, remelted but still linked. The Warforged is called to the horde, to seek its twin, and learn where it came from. Maybe you'll even find that the other half went into another warforged, which the dragon made to seek them out and hunt them down, not realising fully that warfoged are sentient and not just golems, so it could be that the evil hunter half-brother can be persuaded not to go back to the dragon, because it will rip out its heart.

Also, you don't have to explain it. In fact, I would suggest not doing so in game. Partly because it then makes things too much about one PC, and partly because it's unnecessary.

The PC has inherent magic. It's dragon related. If they want to make up a backstory explanation, work it out with them so it fits your worldbuilding. If they don't, it's fine. Not everything needs to have an explanation beyond "that's something that happens".

I agree with jl8e you don’t need to fill in the details. But if you want to, maybe this warforged was created by a dragon. Some of it’s creator’s essence entered the warforged, voila, draconic sorcerer.

Quote from FOODMANIA >>

One of my players is playing a warforged sorcerer draconian bloodline but as they are built they don’t have blood. One of my quests for my players is a background quest about them so to maybe explain how they got magic although I’m not sure how to do it. 

 
If the player hasn't come up with anything themselves to explain the origin of their magic, then maybe viewing it as a 'draconic heritage' rather than a 'draconic bloodline' might give you both some ideas