This paper proposes a reference steering wheel torque map and a torque tracking algorithm via steer-by-wire to design the targeted steering feel. The reference steering wheel torque map is designed using the measurement data of rack force and steering characteristic of a target performance of the vehicle at sinusoidal and transition steering test. Since the target performance of the vehicle is only tested in nominal road condition, various road conditions such as disturbances and tire-road friction are not considered. Hence, the measurement data of the rack force of reflecting the road conditions in the reference steering wheel torque map have been used. The rack force is the net force which consists of tire aligning moment, road friction force and normal force on the tire kingpin axis. A motor and a magnetorheological damper are used as actuators to generate the desired steering feel using the torque tracking algorithm. The torque tracking algorithm is composed of feedforward control and feedback control. The feedforward control uses the plant dynamics to compensate for the torque from the moment of inertia and the viscous friction of the steering system and the feedback control uses an adaptive sliding mode control methodology to compensate for the error between the steering wheel torque and the reference wheel torque in this tracking algorithm. The performance of the proposed controller was evaluated with the sinusoidal and transition tests using computer simulations. By using this proposed control algorithm in steer-by-wire system, the steering feel close to that of a conventional motor driven steer system has been successful obtained.