This study extends the research on self-consistent effective-one-body theory of a real spinless two-body system based post-Minkowskian approximation (Sci. China-Phys. Mech. Astron. 65, 100411 (2022)) to case binary for spinning black holes. An effective rotating metric and an improved Hamiltonian hole binaries are constructed. The decoupled equation null tetrad component gravitational perturbed...