Quantum entanglement is one of the fundamental correlations between particles that has not yet been confirmed with high-energy photons. Quantum electrodynamics (QED) predicts that annihilation photons produced by the decay of the singlet state of positronium (Ps) atoms are entangled in their polarization. Since these photons have an energy of 511 keV, there is no polarizer to measure the polarization of these photons. However, the direction of the scattering photons when interacting with an electron via the Compton process depends strongly on the polarization of the photon. Therefore, Compton scattering can be used as a polarization analyser. The polarization direction of the photon can be defined as the cross product of the momentum vector of the incident and scattered photon. By measuring the polarization of annihilation photons originating from Ps decays, their polarization correlation can be determined. Measuring this correlation will for the first time, will answer the open question of studying quantum entanglement in high-energy photons. Moreover, it also have potential applications in PET imaging, where the quality of image reconstruction directly depends on the selection of pure annihilation photons, which can be separated based on the strength of the polarization correlation. In this paper, we report on the method for determining the polarization correlation of annihilation photons using the J-PET detector.