This paper reported on the design process of a novel discrete-time integral terminal sliding mode control (DITSMC) scheme and its implementation on a precision micro-motion system, which is driven by piezoelectric actuators. By considering the piezoelectric nonlinearities in terms of hysteresis and drift effects as a lumped disturbance, a robust DITSMC scheme is devised and its stability is proved. The proposed digital control strategy is developed based on the system's output feedback alone, whereas the knowledge on system states is not needed. Hence, it is easy to realize for rapid prototyping application. Comparative experimental investigations show that the designed DITSMC controller is superior to conventional PID controller in motion tracking task. Moreover, the presented control can be easily extended to other precision motion systems as well.