A device model for tunnel injection and extraction of spin-polarized charge carriers between ferromagnetic contacts and organic semiconductors with disordered molecular states is presented. Transition rates for tunneling are calculated based on a transfer Hamiltonian. Transport in the bulk semiconductor is described by macroscopic device equations. Tunneling predominantly involves organic molecular levels near the metal Fermi energy, and therefore typically in the tail of the band that supports carrier transport in the semiconductor. Disorder-induced broadening of the relevant band plays a critical role for the injection and extraction of charge carriers and for the resulting magneto-resistance of an organic semiconductor spin valve.