The low crystal symmetry of rhenium disulphide (ReS2) leads to the emergence of dichroic optical and optoelectronic response, absent in other layered transition metal dichalcogenides, which could be exploited for device applications requiring polarization resolution. To date, spectroscopy studies on the optical response of ReS2 have relied almost exclusively in characterization techniques involving optical detection, such as photoluminescence, absorbance, or reflectance spectroscopy. However, to realize the full potential of this material, it is necessary to develop knowledge on its optoelectronic response with spectral resolution. In this work, we study the polarization-dependent photocurrent spectra of few-layer ReS2 photodetectors, both in room conditions and at cryogenic temperature. Our spectral measurements reveal two main exciton lines at energies matching those reported for optical spectroscopy measurements, as well as their excited states. Moreover, we also observe an additional exciton-like spectral feature with a photoresponse intensity comparable to the two main exciton lines. We attribute this feature, not observed in earlier photoluminescence measurements, to a non-radiative exciton transition. The intensities of the three main exciton features, as well as their excited states, modulate with linear polarization of light, each one acquiring maximal strength at a different polarization angle. We have performed first-principles exciton calculations employing the Bethe-Salpeter formalism, which corroborate our experimental findings. Our results bring new perspectives for the development of ReS2-based nanodevices. © 2023 The Author(s). Published by IOP Publishing Ltd.