We investigate the excitonic transitions in single-and few-layer MoSe2 phototransistors by photocurrent spectroscopy. The measured spectral profiles show a well-defined peak at the optically active (bright) A(0) exciton resonance. More interestingly, when a gate voltage is applied to the MoSe2 to bring its Fermi level near the bottom of the conduction band, another prominent peak emerges at an energy 30 meV above the A(0) exciton. We attribute this second peak to a gate-induced activation of the spin-forbidden dark exciton transition, AD(0). Additionally, we evaluate the thickness-dependent optical bandgap of the fabricated MoSe2 crystals by characterizing their absorption edge.