Is it possible to sprain your own ankles using just your hands?

Yes: Theoretically possible though unlikely for one to sprain their own ankle with the power of their own hands.

I suppose: I am not really sure why you would want to do that, but theoretically I suppose so.

Roll over Beethoven.: I guess that just about anything is possible with time and persistence. The feet would not be an easy one, if it was , every one would probably be doing it.

Sure,: it is theoretically possible to injure yourself in that manner.

Yes, But Don't: Yes, its possible by over supinating but dont do that. Once the ligaments loose their integrity and attenuate, its hard for then to heal and return to what it was.