This paper presents an under-actuated robotic hand inspired by the ligamentous structure of the human hand for a prosthetic application. The joint mechanisms are based on the concept of a tensegrity structure formed by elastic strings. These rigid bodies and elastic strings in the mechanism emulate the phalanx bones and primary ligaments found in human finger joints. As a result, the proposed hand inherently possesses compliant characteristics, ensuring robust adaptability during grasping and when interacting with physical environments. For the practical implementation of the tensegrity-based joint mechanism, we detail the installation of the strings and the routing of the driving tendon, which are related to extension and flexion, respectively. Additionally, we have designed the palm structure of the proposed hand to facilitate opposition and tripod grips between the fingers and thumb, taking into account the transverse arch of the human palm. In conclusion, we tested a prototype of the proposed hand to evaluate its motion and grasping capabilities.