In the circular photogalvanic effect, circularly polarized light can produce a direct electron photocurrent in metals, and the direction of the current depends on the polarization. We suggest that an analogous nonlinear effect exists for antiferromagnetic insulators wherein the total spin of light and spin waves is conserved. In consequence, a spin angular momentum is expected to be transferred from photons to magnons so that a circularly polarized electromagnetic field will generate a direct magnon spin current. The direction of the current is determined by the helicity of the light. We show that this resonant effect appears as a second-order light-matter interaction. We find also a geometric contribution to the spin photocurrent, which appears for materials with complex lattice structures and Dzyaloshinskii-Moriya interactions.