Harnessing tailored disorder for broadband light scattering enables high-resolution signal analysis in nanophotonic spectrometers with a small device footprint. Multiple scattering events in the disordered medium enhance the effective path length which leads to increased resolution. Here we demonstrate an on-chip random spectrometer cointegrated with superconducting single-photon detectors suitable for photon-scarce environments. We combine an efficient broadband fiber-to-chip coupling approach with a random scattering area and broadband transparent silicon nitride waveguides to operate the spectrometer in a diffusive regime. Superconducting nanowire single-photon detectors at each output waveguide are used to perform spectral-to-spatial mapping via the transmission matrix at the system, allowing us to reconstruct a given probe signal. We show operation over a wide spectral range with sensitivity down to powers of −111.5 dBm in the telecom band.