The Mott scattering in the presence of a linearly polarized laser field is investigated in the first Born approximation. The theoretical results indicate that at medium and large scattering angles, a large amount of multiphoton processes take place in the course of scattering. The photoabsorption (inverse bremsstrahlung) predominates the photoemission (bremsstrahlung). The sum rule for the multiphoton cross sections is notably violated. When the laser polarization deviates from the incident direction, the laser-modified (summed) cross section shows a considerable dependence on the azimuthal angle of the scattered electron. The dependencies of the cross section on the field strength, the frequency, the polarization direction, and the electron-impact energy are studied.