The effect of the space-time curvature on the relative position angle Δ between the vector of radio waves and the direction of maximum elongation of an extended radiosource is studied during propagation of radiation from the source to the observer. A detailed analysis is carried out for the Gödel type cosmological model. It is found that the rotation of the Universe cannot induce a Birch-type anisotropy with Δ proportional to cos θ, where θ is the angle between the direction of the ray and the rotational axis. An anisotropy with Δ proportional to sin2 θ should be expected. In the case of a Gödel-type model, we have calculated the change in the eccentricity of the ellipse of the source image relative to the eccentricity of the real object.