Applications that use the orbital angular momentum (OAM) of light show promise for increasing the bandwidth of optical communication networks. However, direct photocurrent detection of different OAM modes has not yet been demonstrated. Most studies of current responses to electromagnetic fields have focused on optical intensity- related effects, but phase information has been lost. In this study, we designed a photodetector based on tungsten ditelluride (WTe2) with carefully fabricated electrode geometries to facilitate direct characterization of the topological charge of OAM of light. This orbital photogalvanic effect, driven by the helical phase gradient, is distinguished by a current winding around the optical beam axis with a magnitude proportional to its quantized OAM mode number. Our study provides a route to develop on-chip detection of optical OAM modes, which can enable the development of next-generation photonic circuits.