Tensegrity structures have been widely explored for their lightweight, high-stiffness, and foldable properties. These unique characteristics have enabled their application in various fields including robotics. Tensegrity robots have demonstrated diverse locomotion modes offering versatile solutions for navigation in complex environments. Recent efforts in bio-inspired robotics have led to designs mimicking the movement of natural organisms, such as earthworms. However, existing designs, particularly those utilizing motor-pulley mechanisms for robot body contraction, face significant challenges due to their bulky actuation systems that reduce locomotion efficiency. This paper introduces a novel tensegrity robot, “Tensiworm,” inspired by the peristaltic locomotion of an earthworm. Composed of three icosahedron tensegrity unit cells connected in series, the Tensiworm robot employs a sequential contraction and relaxation mechanism driven by active cable members made of shape memory actuators. This innovative design achieves a 59.13% folding ratio and weighs only 46.9 grams. The robot can travel a distance equal to its body length in approximately ten cycles with an average speed of 10.01 mm per minute. Furthermore, the use of thinner, flexible structural members broadens possibilities for development of millimeter-scale tensegrity robots, which hold significant potential for biomedical applications, including in-vivo testing and targeted drug delivery.