High-precision tension control is very important for industrial production. Benefit from the unique property of magnetorheological (MR) fluid, a MR clutch is a potential device in a tension control system due to its fast response and large output dynamics. In this paper, based on the detailed analysis of axial magnetic induction intensity generated by the coil along the radial distribution, a shear-mode MR clutch with uniform magnetic field distribution along the radial direction is proposed for the tension control system. A theoretical model of torque transmission and a magnetic circuit were derived, and a magnetostatic simulation was carried out to validate the effectiveness of the proposed circuit design. Experimental evaluation was conducted to investigate the static and dynamic transmission torque property. Finally, a proportional-integral-differential controller was designed to regulate the output torque. Experimental testing demonstrated the effectiveness and practical feasibility of the MR clutch in tension control.