This paper considers the problem of designing an engagement controller for a clutch actuator system having a self-energizing mechanism. Since such a system includes a torque amplification mechanism, parametric uncertainties in the model may lead to large erroneous results in the clutch torque controller. To compensate this undesirable effect, adaptive sliding-mode control is applied based on the actuator position tracking. Estimations of the disk friction coefficient and actuator motion parameters are employed to control the engagement torque properly. The disk friction coefficient adaptation provides online stiffness inference for the engagement force while in contact. Moreover, the unstructured disturbance is also compensated by a disturbance observer. Experimental verifications show the improved performance of the developed control method.