The aim of this study was to make a measurement setup that can measure polarization correlations of photons generated in positron annihilation. The measuring principle was based on the fact that in Compton scattering polarized photons have a preferred direction of scattering relative to the direction of the initial polaraization. A measurement setup was made consisting of four cylindrical scintillation detectors, two BaF2 and two LSO detectors. BaF2 detectors were used for scattering of the annihilation photons obtained from the radioactive isotope of sodium 22Na, while the detection of Compton scattered photons was done using LSO detectors. Signals were measured and analyzed digitaly, a DRS4 digitizer was used for measurement. Measurements have found that photons scatter more often by a factor ρ = (1:9 ± 0:2 ± 0:5) in planes that are perpendicular to each other than in the same plane, which shows the existence of the correlation of their polarization, and is consistent with theoretical predictions. It also confirms that this simple measurement setup can measure polarization correlations. The radiation that occurs in positron annihilation has the most well-known practical application in medicine (medical imaging). Positron emission tomography (PET) is based precisely on the principle of detecting gamma radiation, which is produced by positron annihilation. Measuring the polarization correlations of photons obtained from positron annihilation opens the possibility of raising the quality of images obtained by PET devices.