The spectral analysis of light Rayleigh scattered by monodisperse solutions of rigid, anisotropic macromolecules in the reorienting electric field of a laser beam is presented. Formulas for the spectral lineshapes of the polarized and depolarized intensities of scattered light are derived, taking into account the rotational and translational diffusion of the macromolecules in the laser field, From our numerical computations, the influence of the shape and size of the macromolecules and the influence of the reorientation parameter of their polarizability ellipsoid on the lineshapes of the respective scattered light components at a low degree of reorientation in the laser field are determined.