We present fully general-relativistic numerical evolutions of self-gravitating tori around spinning black holes with dimensionless spin a/M=0.7 parallel or antiparallel to the disk angular momentum. The initial disks are unstable to the hydrodynamic Papaloizou-Pringle instability which causes them to grow persistent orbiting matter clumps. The effect of black hole spin on the growth and saturation of the instability is assessed. We find that the instability behaves similarly to prior simulations with nonspinning black holes, with a shift in frequency due to spin-induced changes in disk orbital period. Copious gravitational waves are generated by these systems, and we analyze their detectability by current and future gravitational wave observatories for a large range of masses. We find that systems of 10 M⊙¿relevant for black hole-neutron star mergers¿are detectable by Cosmic Explorer out to ∼300  Mpc, while DECIGO (LISA) will be able to detect systems of 1000 M⊙ (105 M⊙)¿relevant for disks forming in collapsing supermassive stars¿out to cosmological redshift of z∼5 (z∼1). Computing the accretion rate of these systems we find that these systems may also be promising sources of coincident electromagnetic signals.