Thermally activated shape memory alloy (SMA) actuators are direct-driven and produce high power density with design versatility. However, beyond their linear actuation in spring forms there is little variety and their application in robotics is limited by the challenging characterization of the actuator. In this paper we introduce a novel low-profile torsional SMA actuator design, and its comprehensive mechanical performance characterization for centimeter-scale robotic applications. We determine the thermo-mechanical model of the actuator with full characterization experiments with load, without load, and in blocked conditions to analyze actuator performance in robotic applications. We also illustrate its application in an origami robot with closed-loop control of the actuators. From the performance tests we have modeled and demonstrated the functional capacity of this low weight torsional actuator and have possibly shown the maximum physical and material limits of an SMA that produces 34.1 mNm torque and has a torque-to-weight ratio of 486 mNm/g.