Accurate knowledge of the input torque in wind turbine gearboxes is key to improving their reliability. Traditionally, rotor torque is measured using strain gauges bonded to the shaft. Transferring the resulting signal from the rotating shaft to a stationary data acquisition system while powering the sensing devices is complex and costly. The magnitude of the torques involved in wind turbine gearboxes and the high stiffness of the input shaft pose additional difficulties. This paper presents a new alternative method to measure the input torque in wind turbine gearboxes based on deformation measurements of the static first-stage ring gear. We have measured deformation using fiber-optic strain sensors based on fiber Bragg gratings because of their advantages compared to conventional electrical strain gauges. The present study was conducted on a Siemens Gamesa Renewable Energy gearbox with a rated power of 6 MW, in which a total of 54 fiber-optic strain sensors were installed on the outer surface of the first-stage ring gear. The gear mesh forces between the planets and the ring gear cause measurable deformations on the outer surface of the stationary ring gear. The measured strains exhibit a dynamic behavior. The strain values change depending on the relative position of the strain sensors to the planet gears, the instantaneous variations of the input torque, and the way load is shared between planets. A satisfactory correlation has been found between the strain signals measured on the static ring gear and torque. Two signal processing strategies are presented in this paper. The first procedure is based on the peak-to-peak strain values computed for the gear mesh events, and therefore torque can only be estimated when a gear mesh event is detected. The second signal processing procedure combines the strain signals from different sensors using a Coleman coordinate transformation and tracks the magnitude of the fifth harmonic component. With this second procedure, it is possible to estimate torque whenever strain data of all sensors are available, leading to an improved frequency resolution up to the sampling frequency used to acquire strain data. The method presented in this paper could make measuring gearbox torque more cost-effective, which would facilitate its adoption in serial wind turbines and enable novel data-driven control strategies, as well as a more accurate assessment of the consumed fatigue life of the gearboxes throughout their operation.