Polarization-dependent extended x-ray absorption fine structure (PD-EXAFS) measurements have been made on a single-crystal 1000-Angstrom-thick Co film deposited on (100) diamond. By comparing the EXAFS signals corresponding to the in-plane and out-of-plane structure relative to the film plane, we clearly determine that the film does establish the face centered cubic (fcc) phase. Distinguishing between the hcp and fcc phases can thus be performed by qualitatively noting the polarization dependence of the Fourier transform peak amplitudes corresponding to the third and fourth coordination shells. This EXAFS study shows that the Co film studied here is unambiguously in the fcc phase. The Fourier transform peaks corresponding to the first nearest neighbors, parallel and perpendicular to the film, have been compared. Results indicate less than a 0.0075 Angstrom difference between in-plane and out-of-plane bondlengths, no significant change in coordination number and less than a 0.001 Angstrom(2) difference in EXAFS Debye-Waller factors. All of these results indicate no tetragonal distortion of the fcc Co crystal lattice. This technique should prove valuable in future studies when trying to determine the crystallinity of thin films.