We demonstrate the feasibility of high-resolution terahertz gas spectroscopy based on the external optical feedback effect in a quantum-cascade laser. Tuning the frequency of the quantum-cascade laser across a molecular absorption line of CH3OH leads to a reduction of the optical feedback, which can be detected by monitoring the voltage across the quantum-cascade laser. This method provides a high spectral resolution and a sensitivity comparable to that obtained with a cryogenically cooled Ge:Ga photoconductive detector.