A series elastic actuator (SEA) consists of an actuator in series with a compliant element. By measuring and controlling the displacement of the compliant element, an SEA provides better forward and inverse force control accuracy than traditional stiff actuators. SEAs are suitable for rehabilitation robots that need to interact safely with human. Most SEAs use brushless DC motors as the actuators. The merit of using stepper motors as the actuators has not been explored. Stepper motors have much higher torque-to-weight ratios than DC motors. With proper rotor position feedback, stepper motors can achieve smooth and accurate dynamic response similar to brushed or brushless DC motors. This work develops an upper limb rehabilitation exoskeleton with five degrees-of-freedom for the wrist and elbow. Taking advantage of the proposed actuator, the exoskeleton can be lightweight and compact while the performance is comparable or better than existing designs. This exoskeleton with optimized dimensions can produce large torque and motion output while the motors are placed parallel to the forearm and the elbow joint. Forward and inverse force tracking responses of the series elastic stepper motor will be demonstrated to show its force control performance. We expect that the results presented here can provide an alternative for the actuator selection of rehabilitation robots when higher torque-to-weight ratio is required.