Circular dichroism spectroscopy is known to provide important insights into the interplay of different degrees of freedom in quantum materials, and yet spectroscopic study of the optoelectronic responses of quantum materials to structured optical fields, such as light with finite spin and orbital angular momentum, has not yet been widely explored, particularly at cryogenic temperature. Here we demonstrate the design and application of a novel instrument that integrates scanning spectroscopic photocurrent measurements with structured light of controlled spin and orbital angular momentum. For structured photons with wavelengths between 500 nm to 700 nm, this instrument can perform spatially resolved photocurrent measurements of two-dimensional materials or thin crystals under magnetic fields up to $\pm$ 14 Tesla, at temperatures from 300 K down to 3 K, with either spin angular momentum $\pm \hbar$ ororbital angular momentum $\pm \ell \hbar$ (where $\ell$=1,2,3... is the topological charge), and over a (35 $\times$ 25) $\mu m^2$ area with ~ 1 $\mu m$ spatial resolution. These capabilities of the instrument are exemplified by magneto-photocurrent spectroscopic measurements of monolayer 2H-$MoS_2$ field-effect transistors, which not only reveal the excitonic spectra but also demonstrate monotonically increasing photocurrents with increasing |$\ell $| as well as excitonic Zeeman splitting and an enhanced Land\'e g-factor due to the enhanced formation of intervalley dark excitons under magnetic field. These studies thus demonstrate the versatility of the scanning photocurrent spectrometry for investigating excitonic physics, optical selection rules, and optoelectronic responses of novel quantum materials and engineered quantum devices to structured light.