The conditions of the exosphere of Mercury constitute a prime example of a magnetosphere subject to space weather. We aim at improving the diagnostic of the physical conditions of Na atoms in the exosphere of Mercury, with particular emphasis in the possibility of inferring the magnetic field through polarimetry of the Na D emission lines. We performed spectropolarimetry of the Na D emission lines in the exosphere of Mercury at two different ranges of phases of the planet and interpreted them under present models of resonance scattering polarization applied to the Na atom. We measured successfully the polarization of the Na D2 line while no polarization was seen in D1, as expected. The measured polarization varies with the phase angle but it is roughly a factor two smaller than expected from an isolated emitting atom. Depolarization due to the presence of optical depth explains this factor two and is the most probable explanation for this discrepancy. A framework for the observation of polarization in the emission lines of the exosphere and its interpretation is laid. This opens the possibility to use these measurements for diagnostic of the physical conditions in the exosphere of Mercury, and eventually to infer the magnetic field of Mercury and its variability from observations made with ground telescopes.