In this work, novel Shape Memory Alloy (SMA)-based actuators are proposed to provide angular displacements in both clockwise and counter-clockwise directions with compliance. A bidirectional SMA rotating actuator is fabricated using a rotating frame and two SMA wire-based actuating units similar to human skeletal muscle systems without any additional complicated rotational driving mechanism. These actuating units are activated independently to provide bidirectional rotary motions by using sequentially coordinated electrical inputs. The mechanical, thermal, and electrical properties of the bidirectional SMA rotating actuator are also characterized experimentally. The design and manipulation of the proposed actuator are experimentally verified with simple open-loop and closed-loop control strategies.