We revisit the lamp-post geometry of the black-hole accretion disc with a primary illuminating source on the rotational axis. The primary X-ray power-law radiation is Compton reflected from the disc towards the observer. The gravitational field of a rotating black hole influences the photon properties on its way from the primary source to the disc and from the primary source and accretion disc to a distant observer. We study the polarization properties of the radiation how they would be observed in this scenario. The degree and the angle of polarization are examined as functions of the black hole spin, observers inclination angle and the position of the primary source.