We investigate intersubband polaritons formed in the asymmetric quantum well embedded into the semiconductormicrocavity and study the effects of spin-orbit interaction (SOI) acting on intersubband excitations. The spin-orbit interactions of Rashba and Dresselhaus type remove the spin degeneracy of electrons with finite value of in-plane momentum and allow four types of intersubband excitations.While optical spin-flip transitions are suppressed, the spectrum of elementary excitations shows the appearance of upper, lower, and middle polariton branches based on spin-conserving transitions. The accounting of finite photon momentum leads to nonzero average spin projection of electronic ensemble in the first excited subband under continuous wave excitation for both isotropic (Rashba) and anisotropic (Rashba and Dresselhaus) SOI. We predict the possibility of spin-current generation in the considered systems with long coherence length.