I just pressed every key on my keyboard, and was unable to find a button that spins the character. I was able to rotate my character by grabbing it with the mouse and swinging side-to-side, but there's no button as far as I can tell.

You might try going into the settings and turning off the "enable gamepad" toggle; if that works, maybe take a peek at the back of your PC and count the cables to make sure nothing is plugged in that you're not aware of.

I just saw another post a moment ago where the problem was a set of rudder pedals under their desk that they had forgotten was plugged in.