We use polarized photocurrent spectroscopy in a nanowire device to investigate the band structure of hexagonal Wurtzite InAs. Signatures of optical transitions between four valence bands and two conduction bands are observed which are consistent with the symmetries expected from group theory. The ground state transition energy identified from photocurrent spectra is seen to be consistent with photoluminescence emitted from a cluster of nanowires from the same growth substrate. From the energies of the observed bands we determine the spin orbit and crystal field energies in Wurtzite InAs. This information is vital to the development of crystal phase engineering of this important III-V semiconductor.