In this paper, the electronic eigenstates and energy spectra of a two-dimensional system formed by three concentric, coupled, semiconductor quantum rings with a perpendicular magnetic field in the presence and the absence of a single ionized hydrogenic donor impurity are studied. It is found that the magnetic field localizes the electron wave function in the inner rings. The effects of hydrogenic donor on the electronic structure of concentric triple quantum rings are investigated in the both on- and off-center configurations. It is shown that as the donor moves away from the center of the system, the ground state energy decreases monotonically, the degeneracy is lifted and the gap between the energy levels increases. Also, the binding energy of donor impurity increases with increasing magnetic field.