Steady-state screening of resonant magnetic perturbations (RMPs) in a tokamak is analysed taking into account a self-consistent electric field. On the one hand, the self-consistent radial electric field is determined by the balance of the electron radial conductivity in a stochastic magnetic field screened by the plasma and by the neoclassical ion conductivity. On the other hand, the parallel current of electrons, the radial projection of which is balanced by the ion current, determines the screening of RMPs. In this work, the self-consistent electric field and RMP screening are calculated. Two different regimes of screening are found: the 'ion' branch which corresponds to the negative radial electric field and the 'electron' branch for which the electric field is positive. Predictions of the model are compared with the experimental data and results of the simulation with various codes. The corresponding toroidal rotation and pump-out effect are discussed.