How can a singularity rotate?
There are multiple solutions to general relativity which allow for multiple different types of black holes. The "normal" black hole you see most people talk about, with a zero-volume, point singularity, is known as the Schwarzschild black hole. If the black hole is spinning, the Schwarzschild solution no longer applies and you're talking about a different type of black hole. This new type is referred to as a Kerr black hole (other types include the Reissner-Nordstr&ouml;m and the Kerr-Newman).

In a Kerr black hole, the singularity at the center is still zero-volume, but it is no longer a point. Instead it is a disk of zero height, often referred to as a ring singularity or "Ringularity". The angular momentum of the spinning black hole is then the angular momentum around the axis of rotation passing through this ring.