In the present work, we investigate the magnetic properties of the non-interacting diluted magnetic semiconductor (DMS) quantum ring lattices by using the 2D rotator model. We take into account the effect of the exchange interaction and the Zeeman term on the magnetic moment. For this purpose, we derive the exact analytic expression for the single-particle partition function und used it to determine the magnetic moment. We show that the positions of compensation points (points at which the magnetization vanishes at fixed values of the magnetic field strength) in the temperature scale are very sensitive to changes in the Mn concentrations