The effects of a poloidal potential variation of order epsilon, which is likely to be produced during high-power cyclotron wave heating or neutral beam injection, upon neoclassical particle transport and plasma current are studied theoretically, for a realistic tokamak plasma with significant impurity content. Using an approximate collision operator, an analytic procedure is employed to calculate the transport coefficients in the low collisionality regime for a large aspect ratio tokamak. In the presence of carbon impurity, the ion diffusion coefficients are generally found to increase by a factor of approximately 2. Inclusion of the effects of a poloidal electric field is found to result in an increase in the bootstrap current if the potential on the outside of the tokamak is greater than that on the inside [as during ion cyclotron resonance heating (ICRH) or neutral beam injection (NBI)] and the density profiles are more peaked than roughly the square root of the temperature profiles.