Torque and continuous rotation are fundamental methods of actuation and manipulation in rigid robots. Soft robot arms use soft materials and structures to mimic the passive compliance of biological arms that bend and extend. This use of compliance prevents soft arms from continuously transmitting and exerting torques to interact with their environment. Here, we show how relying on patterning structures instead of inherent material properties allows soft robotic arms to remain compliant while continuously transmitting torque to their environment. We demonstrate a soft robotic arm made from a pair of mechanical metamaterials that act as compliant constant-velocity joints. The joints are up to 52 times stiffer in torsion than bending and can bend up to 45°. This robot arm can continuously transmit torque while deforming in all other directions. The arm's mechanical design achieves high motion repeatability (0.4 mm and 0.1°) when tracking trajectories. We then trained a neural network to learn the inverse kinematics, enabling us to program the arm to complete tasks that are challenging for existing soft robots such as installing light bulbs, fastening bolts, and turning valves. The arm's passive compliance makes it safe around humans and provides a source of mechanical intelligence, enabling it to adapt to misalignment when manipulating objects. This work will bridge the gap between hard and soft robotics with applications in human assistance, warehouse automation, and extreme environments.