In this paper, we present a continuously tunable stiffness arm for safe physical human-robot interactions. Compliant joints and compliant links are two typical solutions to address safety issues for physical human-robot interaction via introducing mechanical compliance to robotic systems. While extensive studies explore variable stiffness joints/actuators, variable stiffness links for safe physical human-robot interactions are much less studied. This paper details the design and modeling of a compliant robotic arm whose stiffness can be continuously tuned via cable-driven mechanisms actuated by a single servo motor. Specifically, a 3D printed compliant robotic arm is prototyped and tested by static experiments, and an analytical model of the variable stiffness arm is derived and validated by testing. The results show that the lateral stiffness of the robot arm can achieve a variety of 221.26% given a morphing angle of 90°. The study demonstrates that the compliant link design could be a promising approach to address safety concerns for safe physical human-robot interactions.