Originally Posted by Tim Thompson

But in the case of a black hole, it is not a solid object that is doing the rotating, it is the region of space time that is the black hole that is doing the rotating. Whatever it was that became a black hole, maybe a star, or a whole lot of stars, must have had some angular momentum associated with it. That momentum must still be conserved, it can't just vanish. So the spacetime that is the black hole inherits the angular momentum of the progenitor, and the black hole rotates.