An analytical expression for the electron cyclotron wave driven current density in a uniformly magnetized plasma in which resonant, superthermal electrons (whose velocity is assumed to be nonrelativistic) have a Maxwellian distribution is given. Use has been made of the already known general expression of the absorbed power density to derive the efficiency. The case of interaction at the fundamental cyclotron frequency has been considered in some detail, particularly as far as the first relativistic correction introduced by the resonance condition on the non-relativistic efficiency is concerned. In the case of interaction of an extraordinary mode at the second harmonic a numerical calculation has been performed, and, as a relativistic effect, a non-monotonic dependence of the efficiency on the resonant electrons' temperature for down-shifted resonance and in the regime of oblique propagation is shown.