Twisted string actuators, which are an emerging artificial muscle, efficiently convert rotary motor motion into linear load movement, with advantages like high transmission ratio, compliance, simple structure, and long-distance power transmission. However, the limited range of transmission ratio adjustment remains a challenge. Thus, this paper introduces a novel twisted string actuator design that automatically and continuously adjusts its transmission ratio in response to external loads. Utilizing lightweight hyperelastic slender rods, the twisted string actuator with continuously variable transmission achieves a simple, compact, and cost-effective design. By manipulating the distance between two twisted strings through rod deformation, the transmission ratio continuously adapts to varying load conditions. Mathematical models of the twisted string actuator with continuously variable transmission are derived and experimentally validated, demonstrating a 2.1-fold transmission ratio variation from 0.1 kg to 1.5 kg loads. Application in an anthropomorphic robot finger showcases a 6.2-fold transmission ratio change between unloaded and loaded states. Our twisted string actuator with continuously variable transmission offers unparalleled advantages in weight, cost, simplicity, compliance, and continuous transmission ratio adjustability, making it highly suitable for robotic systems.