We study the properties of axisymmetric and stationary toroidal structures of magnetized perfect fluid with the uniform distribution of specific angular momentum (l = const) orbiting Kerr superspinars whose existence is indicated by string theory. We demonstrate first the specific features of unmagnetized perfect fluid tori occurring in the deep potential well near the surface of the superspinars and enabling clear distinction between Kerr superspinars and Kerr black holes. Then, we investigate the effect of magnetization of the perfect fluid tori and describe the shift of their properties induced by the presence of toroidal magnetic fields.