Programmable materials based on robotic origami have been demonstrated with the capability to fold into 3D shapes starting from a nominally 2D sheet. This concept requires high torque density actuators, flexible electronics and an integrated substrate. We report on two types of stretchable circuitry that are directly applicable to robotic origami: meshed copper traces and liquid-metal-filled channels in an elastomer substrate. Both methods maintain conductivity even at large strains (during stretching) and curvatures (during folding). Both circuit designs are integrated with a tiled origami module actuated by a shape memory alloy actuator. We also integrate a soft curvature sensor into the robotic origami module that measures the full range of motion of the module in real-time.