In this talk, we will discuss the impact of Lorentz symmetry violation on the polarization of the Cosmic Microwave Background (CMB). In the standard model of cosmology, no circular polarization is predicted for CMB radiation. However, if we consider the frame of a moving particle, where Lorentz symmetry is violated, it can result in the emergence of circular polarization in the CMB radiation. This talk will provide a study of this phenomena and its implication for our understanding of the CMB polarization.