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In this study, the torsional vibration analysis of a rotating tapered sandwich beam with a magnetorheological elastomer core has been investigated. The magnetorheological elastomer material is used as a constrained damping layer embedded between two elastic constraining skins in order to improve the vibrational behavior of the sandwich beam. The three layers of the sandwich beam have rectangular cross-sections with symmetric arrangement. The problem formulation is set up based on the torsional theory of rectangular laminated plates. The assumed modes method and the Lagrange equations are used to derive the governing equations of motion of the system. The validity of the presented formulation is confirmed through comparison of the obtained results with those available in the literature. A detailed parametric study is carried out to investigate the effects of applied magnetic field, tapering ratios, magnetorheological elastomer layer thickness, rotating speed, hub radius, and setting angle on the free vibration characteristics of the sandwich beam. The results show that magnetic field intensity, magnetorheological elastomer layer thickness, and tapering ratio have significant influences on the torsional vibrating characteristics of the sandwich beam, and the effects of rotating speed and hub radius are considerable. The setting angle has no substantial effect on the torsional vibration characteristics.