Prior research on robotic hands predominantly focused on high degrees-of-freedom of fully actuated fingers to replicate a natural human hand or on creative designs of underactuated fingers to make a self-adaptive motion. However, in most cases, fully actuated fingers encounter difficulty in grasping unstructured objects, while underactuated fingers experience problems in performing precise grasping motions. To deal with any possible scenarios, this study presents a novel design of an anthropomorphic robotic finger that combines both advantages—fully actuated and self-adaptive (FASA) modes—at once. Actuated by tendons, the FASA finger can grasp objects adaptively and achieve accurate angle positioning with the same mechanical design. Based on the kinetostatic analysis, the guideline for selecting a torsion spring is proposed to fulfill the functions of the FASA finger and attain the optimal design of torsional stiffness, which manifests itself in a series of tests on different configurations of torsion spring. Likewise, the kinematic analysis for the fully actuated mode is given proof that two joints can move independently by controlling two motors. Ultimately, experimental results reflected the capability of the FASA finger to perform not only independent precision angle motion but also self-adaptive grasping motion without any change in mechanical structure.