This paper presents a novel Continuously Variable Transmission (CVT) based on a Twisted String Actuator (TSA), capable of automatically adjusting its Transmission Ratio (TR) in response to external loads. Utilizing lightweight hyperelastic slender rods, the CVT achieves a simple, compact, and cost-effective design. By manipulating the distance between two twisted strings through rod deformation, the TR continuously adapts to varying load conditions. Mathematical models of the TSA-based CVT system are derived and experimentally validated, demonstrating a 2.1-fold TR variation from 0.1 kg to 1.5 kg loads. Application in an anthropomorphic robot finger showcases a 6.2-fold TR change between unloaded and loaded states. Our CVT offers unparalleled advantages in weight, cost, simplicity, compliance, and continuous TR adjustability, making it highly suitable for robotic systems.