The use of travelling waves for the steady-state current drive in an axisymmetric toroidal plasma in the banana regime is studied. The treatment is based on a quasi-linear equation for the electron distribution function, averaged over the period of particle motion along the small azimuth of the torus. It is shown that the trapped electrons do not absorb the energy of the monochromatic (in frequency) RF field and thus only the circulating electrons contribute to the driving current and the absorbed RF power. The current and the absorbed power are calculated by using the electron distribution function obtained for the case of a narrow wave packet, both the toroidial magnetic field and the distortion of the electron distribution with respect to transverse velocities being taken into account. The important role of the marginally circulating electrons is revealed. It is pointed out that the toroidal satellite resonances can affect the RF current drive by spreading and splitting the region of wave-particle interaction.