Abstract
Quantum corrections to electron dynamics in a circularly polarized electromagnetic field are found within the Floquet theory of periodically driven quantum systems. It is demonstrated that emission of photons by an electron rotating under the field leads to the quantum recoil force acting on the electron perpendicularly to the velocity of its forward movement, which differs crucially from the known classical recoil force directed oppositely to the velocity. Physically, such an anomalous radiation reaction arises from the one-loop QED correction to the photon emission and has no analog within the classical electrodynamics. Possible manifestations of this phenomenon are discussed for electrons in strong laser fields.