Application to a tokamak of electron‐cyclotron resonant heating (ECRH) injected at a given poloidal angle will result in a small but important variation of average electron magnetic moment with poloidal angle. This, coupled with the dependence of magnetic field strength on poloidal angle, will result in the transmission of a net toroidal force to the electrons, the direction and magnitude of which depend on the poloidal angle at which the ECRH is injected and the direction of velocity of the electrons by which it is absorbed. The geometries for which this mechanism adds to the Fisch–Boozer mechanism [Phys. Rev. Lett.45, 720 (1980)] are described, as are those for which this mechanism is in opposition. Taking this mechanism into account, it is demonstrated that electrons at large minor radii can be driven with significantly greater efficiency if resonance is on the inboard side of the tokamak than if it is on the outboard side, and the ratio of the two efficiencies is calculated for the case of Coulomb collisionality in the limit of large Larmor radius. The case of turbulence‐dominated collisionality is considered, and a general prediction of the ratio of the efficiency of this drive mechanism to that of the Fisch–Boozer mechanism is presented, in which the ratio of the efficiencies is given in terms of the dependence of the slowing‐down time on velocity. The mechanism described herein provides a significant correction to predictions of current drive efficiency for infinite Larmor radius Coulomb collisionality, and is likely to provide a more significant correction yet for more realistic models of collisionality.