We report on the first elastic hard x-ray scattering experiment where the linear polarization characteristics of both the incident and the scattered radiation were observed. Rayleigh scattering was investigated in a relativistic regime by using a high- Z target material, namely gold, and a photon energy of 175 keV. Although the incident synchrotron radiation was nearly 100% linearly polarized, at a scattering angle of θ = 90 ° we observed a strong depolarization for the scattered photons with a degree of linear polarization of + 0.27 % ± 0.12 % only. This finding agrees with second-order quantum electrodynamics calculations of Rayleigh scattering, when taking into account a small polarization impurity of the incident photon beam which was determined to be close to 98%. The latter value was obtained independently from the elastic scattering by analyzing photons that were Compton-scattered in the target. Moreover, our results indicate that when relying on state-of-the-art theory, Rayleigh scattering could provide a very accurate method to diagnose polarization impurities in a broad region of hard x-ray energies.