Spin waves in antiferromagnets are linearly or circularly polarized. Depending on the polarization, traversing spin waves alter the staggered field in a qualitatively different way. We calculate the drift velocity of a moving domain wall as a result of spin wave-mediated forces and show that the domain wall moves in opposite directions for linearly and circularly polarized waves. The analytical results agree with micromagnetic simulations of an antiferromagnetic domain wall driven by a localized, alternating magnetic field.