Analogous to biological muscles, twisted yarns with the capacity to output torsional torque and reversible rotation are of significant value in the development of soft robotic systems. However, how to achieve large torque while efficiently integrating electrical control elements to the soft actuators remains scientific and engineering challenges. Here, by concentric twisting a flexible silver-plated polyamide strand (SPS) with multi-layer liquid crystal elastomer fibers (LCEFs), a twisted yarn actuator with the skin-core structure that exhibits outstanding rotational motion under the electrical current control is fabricated. It has been proved that this multi-layered twisting structure efficiently improves the actuating performance. The yarn actuator can produce a peak torque of 33.4 N m kg−1 which outperforms reported commercial rotating motors and a specific power density of 21.2 W kg−1 that is comparable to the human skeletal muscle. As conceptual applications, electrical soft rotors and a novel flexible lifter have been successfully constructed based on the twisted yarn actuator, demonstrating precise torque responsiveness and controllability. Furthermore, a smart crawling fabric embedded with the twisted yarn actuators has been weaving fabricated which can crawl forward continuously and achieve the crawling stroke of 19.9 mm in 55 s and a maximum speed of 1.1 mm s−1. The research provides insights for designing soft robots employing fabric structures.