The poloidal electric field generated by electron-cyclotron resonance heating is investigated for a tokamak plasma in the collisionless regime. This poloidal electric field is calculated by solving an adjoint equation to the linearized Fokker-Planck equation with a quasi-linear diffusion term. It is found from this calculation that the magnitude and the sign of the poloidal electric field depend strongly on the values of the inverse aspect ratio, the poloidal angle of the absorption point, the parallel velocity of resonant electrons normalized by the thermal velocity, and the strength of the relativistic correction to the resonance condition.