We report on the observation of the cyclotron-resonance-assisted photon drag effect. Resonant photocurrent is detected in InSb/InAlSb quantum well structures subject to a static magnetic field and excited by terahertz radiation at oblique incidence. The developed theory based on Boltzmann's kinetic equation is in good agreement with the experimental findings. We show that the resonant photocurrent originates from the transfer of photon momentum to free electrons drastically enhanced at the cyclotron resonance.