Bolometers are a powerful means of detecting light. Emerging applications demand that bolometers work at room temperature, while maintaining high speed and sensitivity, properties which are inherently limited by the heat capacity of the detector. To this end, graphene has generated interest, because it has the lowest mass per unit area of any material, while also possessing extreme thermal stability and an unmatched spectral absorbance. Yet, due to its weakly temperature-dependent electrical resistivity, graphene has failed to challenge the state-of-the-art at room temperature. Here, in a departure from conventional bolometry, we use a graphene nanoelectromechanical system to detect light via resonant sensing. In our approach, absorbed light heats and thermally tensions a suspended graphene resonator, thereby shifting its resonant frequency. Using the resonant frequency as a readout for photodetection, we achieve a room-temperature noise-equivalent power (2 pW Hz-1/2) and bandwidth (from 10 kHz up to 1.3 MHz), challenging the state-of-the-art.