The effect on electron cyclotron current drive of the relativistic correction arising from the velocity dependence of the electron cyclotron frequency has been investigated. This correction is shown to be important, particularly for waves propagating close to perpendicular to the magnetic field, for plasmas in the keV range and above. The steady‐state current due to the asymmetric heating mechanism described by Fisch and Boozer has been calculated. The most striking effect of the relativistic correction is that the current driven in the plasma in response to a given wave amplitude is, in an inhomogeneous field, no longer antisymmetric about the cyclotron resonance layer. This means that it is possible to drive a nonzero total current without strong absorption, and also that the total current depends strongly on whether the wave is incident from the low‐field or the high‐field side.