A stable, reliable and well-calibrated beam position monitor (BPM) system is essential for a safe and reproducible operation of accelerators. The BPM system enables the measurement of important machine and beam parameters, such as the Twiss parameters, and helps to avoid damage to accelerator components by high-energy particle beams or radiation. In this paper, we discuss a new BPM calibration scheme tested at the Taiwan Photon Source (TPS). By altering the current in a single horizontal or vertical corrector magnet, we generate an orbit distortion with respect to the nominal reference orbit. The difference orbit is measured by observing the change of the beam position at each BPM pickup location as a function of the corrector current. The analog BPM signals are digitized by analog-to-digital converters (ADC), giving raw, non-calibrated beam position data for each BPM. By comparison of the beam orbit response in terms of raw ADC data from each BPM with the expected beam displacement we can calibrate the beam position monitors. Moreover, because of limited setup time available after a long shutdown, this new procedure acts as a fast, easy way to calibrate the BPM system.