We demonstrate a cavity-enhanced room-temperature magnetic field sensor based on nitrogen-vacancy centers in diamond. Magnetic resonance is detected using absorption of light resonant with the 1042 nm spin-singlet transition. The diamond is placed in an external optical cavity to enhance the absorption, and significant absorption is observed even at room temperature. We demonstrate a magnetic field sensitivity of 2.5 nT/Hz, and project a photon shot-noise-limited sensitivity of 70 pT/Hz for a few mW of infrared light, and a quantum projection-noise-limited sensitivity of 250 fT/Hz for the sensing volume of ∼90 μm×90 μm×200 μm.