The influence of quantum electrodynamics (QED) to the process of radiative electron capture (REC) is investigated in the region of highly relativistic projectile energies by modifying the wave functions according to the Uehling potential. Exact relativistic calculations are employed for the radiative recombination. The deviation from non-QED calculations is found to amount to up to 2% in U⁹²⁺ for a projectile energy of 10 GeV/u and forward emission angles of the emitted photon.