We show that the polarimetry of H$\alpha$ emission in supernova remnant shocks can be powerful diagnostics of cosmic-ray modified shocks (CRMSs). Solving the radiative line transfer problem in collisionless shocks propagating into a partially ionized medium, we find directions of the linearly polarized H$\alpha$ depend strongly on the existence of shock modification; the direction is parallel to the direction of shock travel for the case of the CRMS, while the direction is perpendicular for the case of no modification.