To investigate the effect of vacuum polarization in the Coulomb interaction between hadrons, the relative differential cross section for elastic '^C-^^C scattering at Exs^h^^ MeV has been measured with high precision. The data are compared to theoretical calculations that take into account the contribution of the Uehling potential and other small contributions. Data and calculation agree within 1.5 standard deviations. This constitutes a test of the vacuum polarization on the 7% level.