Electron Bernstein waves are of interest for heating and current drive in spherical tokamaks where the central region of the plasma is not accessible to the ordinary and extraordinary modes. In this paper we adapt an analytical theory of current drive in toroidal geometry developed by Lin-Liu et al (2003 Phys. Plasmas10 4064) to this system. This involves taking account of the fact that the ratio of the Larmor radius to the perpendicular wavelength is not, in general, small for the Bernstein waves and also including the effects of a non-circular plasma cross section. By comparing the results with those of a full Fokker–Planck code, we demonstrate that the analytical method can yield a good approximation to the current drive efficiency in most regimes of practical interest. Since it is much less computationally demanding than using a Fokker–Planck code we suggest that it could be a useful tool for analysing experiments on Bernstein mode current drive in spherical tokamaks.