The gravitational time delay of signals in a gravitational field of a rotating massive body is considered both in a weak field approximation and in a strong field caused by a rotating black hole. The expressions describing the time of propagation of signals are obtained by integrating the light geodesics of the Kerr metric in a frame reference of a distant observer using the Boyer-Lindquist coordinates and assuming that the wave length of radiation is much less than the characteristic scale of the field. The existence of the asymmetry in the time delay is shown depending on the mutual orientation of a photon propagation direction and of the rotation axis. As a result of this asymmetry, the effects of relative time delay are predicted and calculated for the signals focused by a rotating gravitational lens.