The non-Noether conserved quantities (the Hojman conserved quantity) for nonholonomic controllable mechanical systems with relativistic rotational variable mass are discussed. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are discussed respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is presented. The condition under which a non-Noether conserved quantity can be induced by the Mei symmetries and the form of the conserved quantity are obtained. An example is presented to illustrate the application of the result.