Yes, but Starship is a prototype at the moment. And it'd require the Super Heavy to even reach orbit, which will soon begin testing [0].

Additionally, the engineering requirements for long-term life support are significantly more involved than the Dragon capsule.

There's also the testing and certification process for crewed-missions; in non-Elon time, this is likely several years, conservatively speaking [1]. (I'd love to be proven wrong, however!).

[0] https://www.space.com/spacex-starship-super-heavy-booster-ro...

[1] https://arstechnica.com/science/2021/04/five-reasons-why-nas...