The paper presents a method to estimate the inverse of the rotor time constant of the induction motor. Estimation is done using a sliding mode observer which is developed based on the model of the motor in the synchronous reference frame. The method considers that the flux magnitude is known - this is estimated using a voltage model observer. In addition, the field-orientation angle is available; with this, the currents id and iq are used to generate the feedback terms of the observer. The observer needs a speed signal and, since speed should not be measured, it is fed with a speed estimate (which is assumed inaccurate). Under these conditions, it is normal to have an inaccurate output; however, the paper proposes a gains design that allows to reduce the error in the estimated rotor time constant. Simulations and experiments validate the design.