Measuring servo torque
Yes. Motor torque is directly proportional to the current. In the case of a brushless motor, torque is proportional to the phase currents when expressed in a rotating reference frame. This principle is used often in robotics, especially when creating highly dynamic robots, and when used in combination with accurate and precise encoders, can be used even to estimate end effector forces. If your motor manufacturer does not provide you with the torque constant, you can easily obtain it by measuring the motor's velocity constant (the no-load motor speed in RPM divided by the voltage at that speed). The torque constant is proportional to the inverse of the velocity constant.