The Sunyaev-Zel?dovich effect (SZE) is due to the inverse Compton scattering of cosmic microwave background radiation photons by high energy electrons in galaxy clusters. This effect helps to understand the properties of galaxy clusters such as their temperature, ingredients, the distribution of different materials, and in some cases the dynamics of the galaxy clusters. The SZE was mathematically derived by the Kompaneets equation, which was obtained by Boltzmann?s equation. The relativistic form of Kompaneets equation has also developed that increases the precision of the calculations. Next, it was discovered that the polarization of this effect (the polarization of photons during the scattering of electron plasma into galaxy clusters) would also be a novel and useful way to study the physics of clusters. To study the polarization of this effect, we first import the polarization into the Boltzmann equation by performing some tensor calculations. Then we wrote the Boltzmann equation in a covriant form since it consistent with relativity. At the end of this research, it is concluded that by applying relativistic considerations, not only the quadropole of cosmic microwave background radiation is important in the polarization of the SZE, but the octopole term is also effective. With increasing the tempreture of galaxy cluster, the octopole effect is also increasing. According to the calculations performed in this study, for detecting the polarization of the SZE, the current detectors are very weak and therefore detecting this effect is not accessible right now.