Sensorless torsion control is proposed for elastic-joint robots, with the geared drives subject to hysteresis and friction nonlinearities. The concept of the so-called “virtual torsion sensor” uses the motor torque and velocity, inherently available in most industrial robots, for estimating the reactive joint torque and predicting, based thereupon, the nonlinear joint torsion. The dynamics of the elastic-joint robot is described and augmented by a rate-independent torsion–torque hysteresis and nonlinear friction assumed on the side of motor drives. The classical two-degrees-of-freedom robot control, which includes the centralized torque feedforward control and proportional-derivative feedback control, is extended by the virtual torsion sensor in the loop. In particular, we show that the computed joint torsion can be injected in the feedback loop upon the motor position, thus making the control operating in a “virtual” joint output (link) space. The proposed control is experimentally evaluated on a single-joint setup consisting of an actuator with harmonic-drive gear and inertial load under additional impact of gravity.