This paper presents a robotic finger mechanism with a compliant grasp area. A preliminary review of contemporary works and experiments led to the recognition of the primary significance of tactile sensing for a robotic hand in successful grasping operations, especially when compared to traditional robots operating in an unstructured environment. A two-finger hand is proposed with a thumb and an articulated finger both having phalanx area with a compliant surface. A low-cost prototype for lab testing was built with cost-effective market-available components and 3D-printed parts, while still maintaining designed performance and reliability. The proposed design was validated with the prototype that is equipped with a compliant grasp capability though grasp tests whose results show also the performance capability.