The influence of spin-orbit coupling in the unoccupied sp_z quantum well states in ultrathin Co films is investigated by two-photon photoemission spectroscopy with linearly polarized light. The asymmetry of the experimental two-photon photoemission intensities upon magnetization reversal is as large as 10%, which is in striking contrast to expectations based on the weakness of spin-orbit coupling in the observed quantum well states. The magnetic dichroic signal depends strongly on the polarization of the incident light as well as on the spin polarization of the quantum well states. These findings are explained by detailed electronic structure calculations and one-photon photoemission calculations. Our conclusions are supported by analytical considerations. In this way, a detailed picture of spin-orbit coupling in the unoccupied Co/Cu(001) quantum well states is provided.