This paper introduces a self-sensing anthropomorphic robot hand driven by Twisted String Actuators (TSAs). The use of TSAs provides several advantages such as muscle-like structures, high transmission ratios, large output forces, high efficiency, compactness, inherent compliance, and the ability to transmit power over distances. However, conventional sensors used in TSA-actuated robotic hands increase stiffness, mass, volume, and complexity, making feedback control challenging. To address this issue, a novel self-sensing approach is proposed using strain-sensing string based on Conductive Polymer Composite (CPC). By measuring the resistance changes in the strain-sensing string, the bending angle of the robot hand's fingers can be estimated, enabling closed-loop control without external sensors. The developed self-sensing anthropomorphic robot hand comprises a 3D-printed structure with five fingers, a palm, five self-sensing TSAs, and a 3D-printed forearm. Experimental studies validate the self-sensing properties of the TSA and the anthropomorphic robot hand. Additionally, a real-time Virtual Reality (VR) monitoring system is implemented for visualizing and monitoring the robot hand's movements using its self-sensing capabilities. This research contributes valuable insights and advancements to the field of intelligent prosthetics and robotic end grippers.