A torque transfer mechanism is provided for controlling the magnitude of a clutch engagement force exerted on a multi-plate clutch assembly that is operably disposed between a first rotary and a second rotary member. The torque transfer mechanism includes an actuator having a first segment fixed for rotation with the first rotary member and a second segment having a screw thread formed thereon which is rotatably and slidably disposed within a chamber filled with magnetorheological fluid. An electromagnetic coil is disposed in proximity to the chamber and is selectively energized for varying the viscosity of the magnetorheological fluid so as to induce axial movement of the actuator for engaging the multi-plate clutch assembly.