Torsional vibrations may arise in many mechanical engineering applications, and cause a high level of complexities and non-stationarities accordingly. The present study proposes a new signal processing method based on the Recursive Autocorrelation (RAC) function, which can be considered as a reliable fault detection algorithm for rolling bearings in non-stationary operating conditions caused by torsional vibrations. The effectiveness and sensitivities of the proposed method are assessed using experimental data captured from a test rig designed for this purpose. Moreover, a numerically-generated vibration signal model for faulty rolling bearings with a shaft subjected to the twisting oscillations (i.e. torsional vibrations) is also proposed. In addition to the experimental studies, the proposed RAC-based methodology is examined numerically using the proposed signal model. As a result of this work, it is observed that the adverse effects of torsional vibrations in the field of bearing fault detection can be controlled using the RAC-based methodology. Both the experimental and the numerical results presented here confirm the computational advantages of RAC over the available order tracking-based approaches.