Conventional rotary actuators mainly rely on electric or hydraulic/pneumatic motors to convert energy into mechanical motion, making them one of the most widely used actuation methods in industrial manufacturing, robotics, and automation control. However, these traditional actuators often suffer from limitations in operability and applicability due to their complex structures, bulky systems, high energy consumption, and severe mechanical wear. Liquid crystal elastomers (LCEs) have been increasingly used for programmable actuation applications, owing to their ability to undergo large, reversible, and anisotropic deformations in response to external stimuli. In this work, we propose a compact flexible rotary joint (FRJ) based on LCEs. To describe the thermo-mechanical coupled behaviors, a constitutive model is developed and further implemented for finite element analysis (FEA). Through combining experiments and simulations, we quantify the dynamic rotational behavior of the rotor rotating relative to the base driven by the induced strain of the FRJ under cyclic thermal stimuli. The proposed rotary joint features a simple structure, lightweight design, low energy consumption, and easy control. These characteristics endow it with significant potential for miniaturization and integration in the field of soft actuation and robotics.