Optomechanical transduction is demonstrated for nanoscale torsional resonators evanescently coupled to optical microdisk whispering gallery mode resonators. The on-chip, integrated devices are measured using a fully fiber-based system, including a tapered and dimpled optical fiber probe. With a thermomechanically calibrated optomechanical noise floor down to 7 fm/Hz, these devices open the door for a wide range of physical measurements involving extremely small torques, as little as 4×10−20N·m.