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We explore the effect of re-radiation in surface-enhanced Raman scattering (SERS) through polarization-sensitive experiments on self-organized gold nanowires on which randomly oriented Methylene Blue molecules are adsorbed. We provide the exact laws ruling the polarized, unpolarized, and parallel- and cross-polarized SERS Intensity as a function of the field polarizations. We show that SERS is polarized along the wire-to-wire nanocavity axis, independently from the excitation polarization. This proves the selective enhancement of the Raman dipole component parallel to the nanocavity at the single molecule level. Introducing a field enhancement tensor to account for the anisotropic polarization response of the nanowires, we work out a model that correctly predicts the experimental results for any excitation/detection polarization and goes beyond the E(4) approximation. We also show how polarization-sensitive SERS experiments permit one to evaluate independently the excitation and the re-radiation enhancement factors accessing the orientation-averaged non-diagonal components of the molecular Raman polarizability tensor.