This Study investigates the measurement of the circular polarization of the Cosmic Microwave Background (CMB) and those radiofrequency sources which generate circular polarization. First, briefly reviews the thermal history of the universe and the CMB physics. CMB radiation is produced at the last scattering surface (LSS) which is the smoking gun of big bang model. By measuring the fluctuations of the CMB, one can study the physics of early universe. As it is well known, CMB can be polarized due to the Compton scattering and quadruple anisotropy at LSS. It is usually assumed that, CMB is linearly polarized. However, circular polarization is generally assumed for the CMB due to some new physics at LSS. In this study, the CMB polarization is parameterized using the Stokes parameters, I, Q, U and V that I parameterize the intensity, Q and U parameterize the linear polarization and V parameterize the circular polarization. Recent measurements have shown that 10 percent of CMB radiation is linearly polarized. The next chapter, reviews and describes the polarization of radio sources such as M81 and SgrA*. Some radio observations have shown that M81 and SgrA* involve small amount of circular polarization. In this study, different methods of detection of their circular polarization are reviewed. Then, to measure the CMB circular polarization, some experiments were done. Among these experiments, the main focus is on the recent experiment is called SPIDER. It is done to measure the circular polarization and discuss its recent constraints. Finally, the calculation of error on the Stokes parameters when the parameters were measured was done. First, it is assumed that there is no circular polarization. It is shown how systematic errors can distort the observed CMB polarization. Then, the method is extended and considered the Stokes Parameter V. It is shown how systematic effects can contaminate any future measurements of circular polarization.