The high precision position tracking in many industrial and scientific devices is vital for various tasks. Among these, periodic signals are commonly used in the condition that the references are given or planned in advance. In this paper, a discrete-time integral terminal sliding mode based repetitive control (DTITSMRC) is developed for periodic motion tracking. The discrete-time integral terminal sliding surface is employed for a fast convergence, and the repetitive control law with this sliding surface is integrated into the control scheme to further improve the performance through learning the information of the previous period. The quasi sliding mode band (QSMB) constrained for any initial state and the finite-time steps to QSMB with DTITSMRC are proven respectively. The simulation results on a discrete-time system demonstrate the effectiveness on periodic motion tracking for various signals.