A current drive scheme for tokamaks, involving oscillating the Ohmic heating (OH) circuit, is proposed. This scheme is based upon the experimentally observed anomalous skin penetration during the start‐up phase of tokamaks. Analytic and numerical results indicating feasibility are shown and scaling of steady‐state current and power dissipated with frequency and plasma resistivity is presented. An explanation is given of why this scheme should work, in spite of the fact that the external circuit supplies no magnetic helicity. This scheme is potentially more efficient in terms of current generated per unit power dissipated than other current drive schemes. It is shown that a resistive magnetohydrodynamic (MHD) activity responsible for anomalous current penetration, and therefore required for the success of this current drive scheme, must be fully three dimensional. Finally, a comparison of the effectiveness of this scheme with that of F‐&THgr; pumping in reversed‐field pinches (RFP’s) is presented.