In this study, a new method was presented for the detection of a static eccentricity fault in a closed loop operating induction motor driven by inverter. Contrary to the motors supplied by the line, if the speed and load, and therefore the amplitude and frequency, of the current constantly change then this also causes a continuous change in the location of fault harmonics in the frequency spectrum. Angular Domain Order Tracking analysis (AD-OT) is one of the most frequently used fault diagnosis methods in the monitoring of rotating machines and the analysis of dynamic vibration signals. In the presented experimental study, motor phase current and rotor speed were monitored at various speeds and load levels with a healthy and static eccentricity fault in the closed loop driven induction motor with vector control. The AD-OT method was applied to the motor current and the results were compared with the traditional FFT and Fourier Transform based Order Tracking (FT-OT) methods. The experimental results demonstrate that AD-OT method is more efficient than the FFT and FT-OT methods for fault diagnosis, especially while the motor is operating run-up and run-down. Also the AD-OT does not incur any additional cost for the user because in inverter driven systems, current and speed sensor coexist in the system. The main innovative parts of this study are that AD-OT method was implemented on the motor current signal for the first time.