Accretion onto black holes in wind-fed binaries and in collapsars forms small rotating discs with peculiar properties. Such ``mini-discs'' accrete on the free-fall time without help of viscosity and nevertheless can have a high radiative efficiency. The inviscid mini-disc model was previously constructed for a non-rotating black hole. We extend the model to the case of a spinning black hole, calculate the structure and radiative efficiency of the disc and find their dependence on the black hole spin. If the angular momenta of the disc and the black hole are anti-aligned, a hydrodynamic analog of Penrose process takes place.