  Analog physics allows simulating inaccessible objects, such as black holes,
in the lab. We propose to implement an acoustic Kerr black hole with quantized
angular momentum in a polariton Bose-Einstein condensate. We show that the
metric of the condensate is equivalent to the Kerr's one, exhibiting a horizon
and an ergosphere. Using topological defects as test particles, we demonstrate
an analog Penrose effect, extracting the rotation energy of the black hole. The
particle trajectories are well described by the time-like geodesics of the Kerr
metric, confirming the potential of analog gravity.
