The formation of a superstructure - with a related Moir\'e pattern - plays a crucial role in the extraordinary optical and electronic properties of twisted bilayer graphene, including the recently observed unconventional superconductivity. Here we put forward a novel, interdisciplinary approach to determine the Moir\'e angle in twisted bilayer graphene based on the photonic spin Hall effect. We show that the photonic spin Hall effect exhibits clear fingerprints of the underlying Moir\'e pattern, and the associated light beam shifts are well beyond current experimental sensitivities in the near-infrared and visible ranges. By discovering the dependence of the frequency position of the maximal photonic spin Hall effect shift on the Moir\'e angle, we argue that the latter could be unequivocally accessed via all-optical far-field measurements. We also disclose that, when combined with the Goos-H\"anchen effect, the spin Hall effect of light enables the complete determination of the electronic conductivity of the bilayer. Altogether our findings demonstrate that sub-wavelength spin-orbit interactions of light provide a unprecedented toolset for investigating optoelectronic properties of multilayer two-dimensional van der Waals materials.