Wereport on the first elastic hard x-ray scattering experiment where the linear polarizationcharacteristics of both the incident and the scattered radiation were observed. Rayleigh scattering wasinvestigated in a relativistic regime by using a high-Z target material, namely gold, and a photon energyof 175keV. Although the incident synchrotron radiation was nearly 100% linearly polarized, at ascattering angle of q = 90we observed a strong depolarization for the scattered photonswith adegree of linear polarization of +0.27%  0.12%only. This finding agreeswith second-orderquantum electrodynamics calculations of Rayleigh scattering, when taking into account a smallpolarization impurity of the incident photon beam which was determined to be close to 98%. Thelatter value was obtained independently from the elastic scattering by analyzing photons that wereCompton-scattered in the target. Moreover, our results indicate that when relying on state-of-the-arttheory, Rayleigh scattering could provide a very accurate method to diagnose polarization impuritiesin a broad region of hard x-ray energies.