Quantum mechanics itself is actually completely deterministic. It's just certain interpretations, like Copenhagen, that unnecessarily introduce nondeterminism. The Many Worlds interpretation is one that doesn't have that property.

In any case, I don't think determinism and free will have much to do with each other. Eg a classically random fair coin is non-deterministic, but can hardly be said to have free will.

In the other direction, a Turing machine is completely deterministic, but in general you can't predict what it does (without running it.)

If you want to bring up quantum mechanics, I think the no-cloning theorem is more important: no one can learn everything about you in order to 100% simulate and predict you. (Which is what you'd need for the Turing machine. And humans are at least as complicated as Turing machines.)