The effects of optical feedback (OF) in lasers have been observed since the early days of laser development. While OF can result in undesirable and unpredictable operation in laser systems, it can also cause measurable perturbations to the operating parameters, which can be harnessed for metrological purposes. In this work we exploit this 'self-mixing' effect to infer the emission spectrum of a semiconductor laser using a laser-feedback interferometer, in which the terminal voltage of the laser is used to coherently sample the reinjected field. We demonstrate this approach using a terahertz frequency quantum cascade laser operating in both single- and multiple-longitudinal mode regimes, and are able to resolve spectral features not reliably resolved using traditional Fourier transform spectroscopy. We also investigate quantitatively the frequency perturbation of individual laser modes under OF, and find excellent agreement with predictions of the excess phase equation central to the theory of lasers under OF.