Ohkawa has proposed a tokamak current‐drive scheme [Comm. Plasma Phys. Controlled Fusion12, 165 (1989)], which relies on the injection of circularly polarized magnetohydrodynamic waves. It is shown here that the favorable current‐drive efficiency predicted by Ohkawa is not attained because excessive power is dissipated by the fluctuating fields. The ratio of power absorbed by the plasma to the dc Ohmic power required to drive the same current isPabsorbed/POhmic≊4(Ba/b)2, whereBais the static toroidal field strength andbis the strength of the fluctuating field.