The one-dimensional Fisch theory of plasma heating and current drive by high parallel phase velocity waves is generalized to include the effect of a parallel electric field. It is shown that in the presence of an electric field parallel (antiparallel) to the RF current, the power absorption, the RF current and the current drive efficiency increase (decrease). Electric field effects can be strong during current ramp-up or when recharging the transformer in Tokamaks. The results are given in analytical form, allowing direct application to transport modelling.