We study the polarized Surface Enhanced Raman Scattering from randomly oriented molecules adsorbed on near-field coupled gold nanowires. We show that the scattering is polarized always along the wire-to-wire nanocavities. We find the exact angular dependence for the polarized, unpolarized, parallel-and cross-polarized SERS intensity. Finally we develop a model that fits the experimental data and allows to measure the field enhancement and the re-radiation enhancement factors, independently, and retrieve the depolarization ratio of the probe molecules.