bbPress.org

Not really. At least not easily, and there is no existing and easy to use plugin. That said, if you’re dilligent enough and have enough PHP skills you could probably garnish a solution from the threads _ck_ links to here:

Extra dropdown field in registration page

[EDIT chrishajer]

If you have bbPress integrated with WordPress (sharing database and logins), then I strongly suggest using WordPress for registrations as you can theme and plugin to your hearts content there.