Structured vortex light with orbital angular momentum (OAM) shows great promise for high-bandwidth optical communications, quantum information and computing, optical tweezers, microscopy, astronomy, among others. Generating, controlling, and detecting of vortex light by all-electrical means is at the heart of next generation nanophotonic platforms. However, on-chip electrical photodetection of structured vortex light remains challenging. Here, we propose an on-chip photodetector based on 2D broadband thermoelectric material (PdSe2) with a well-designed spin-Hall couplers to directly characterize angular momentum modes of vortex structured light. Photothermoelectric responses in the PdSe2 nanoflake, excited by the focusing surface plasmons, show a magnitude proportional to the total angular momentum modes of the infrared vortex beams, thereby achieving direct detection of spin and orbital angular momentum, as well as the chirality and ellipticity of scalar vortex lights. Our works provide a promising strategy for developing on-chip angular momentum optoelectronic devices, which play a key role in the next-generation high-capacity optical communications, quantum information and computing, imaging, and other photonic systems.