We report the study of the helicity-driven photocurrents in graphene excited by midinfrared light of a CO₂ laser. Illuminating an unbiased monolayer sheet of graphene with circularly polarized radiation generates- under oblique incidence-an electric current perpendicular to the plane of incidence, whose sign is reversed by switching the radiation helicity. We show that the current is caused by the interplay of the circular ac Hall effect and the circular photogalvanic effect. By studying the frequency dependence of the current in graphene layers grown on the SiC substrate, we observe that the current exhibits a resonance at frequencies matching the longitudinal optical phonon in SiC.