Electron Bernstein waves (EBWs) have been confirmed as a suitable choice for plasma heating and current drive generation (electron Bernstein current drive) at densities where the O and X modes find cutoff values. In the present work, an estimation of the efficiency function of current generated for a relativistic distribution function is presented. The arbitrary large values of the refractive index, due to the EBW propagation properties, have also made necessary the expansion of our calculation up to any Larmor radius order. Particle trapping has been included considering the Okhawa effect, and the fractions of power absorbed by trapped and circulating particles separately have been estimated. Future work toward implementation of this method to the ray-tracing code used for realistic TJ-II ray trajectories (TRUBA) is also discussed.