The advent of high-flux-polarized γ-ray sources makes possible the nearly isolated precise measurement of the vacuum contribution, Delbrück scattering, to the elastic scattering of these photons off nuclei. Because of the fact that the elastic scattering of the photons is a coherent summation of four processes and that up to now unpolarized sources have been used, the isolated measurement of Delbrück scattering has not been performed. We show that for the appropriate choice of scattering angles, photon polarization, and energies this scattering can be measured nearly independently of other scattering processes. This makes possible the precise measurement of the vacuum contribution to scattering and the possibility of the detection of new physics.