Compliant mechanisms (CMs) exhibit some excellent mechanical properties and provide numerous innovative solutions for many existing mechanical applications. Among them, planar compliant rotational joints have made substantial contributions to precision engineering. To achieve high-precision positioning with a compliant rotational joint, it is essential to study characteristics such as anti-buckling and constant stiffness. The remote center of motion (RCM) mechanism, with its compact structure and ease of precise control, is expected to enhance overall rigidity and reduce parasitic displacements. Here, we propose a planar anti-buckling compliant rotational joint with a RCM. Static modeling and model validation are conducted for different geometric configurations, including single and combined structures. A distributed configuration with bidirectional anti-buckling properties is selected for optimization. Using a global parameter optimization model, single-objective optimization studies are conducted for three distinct characteristics. Subsequently, a multi-objective optimization model for constant stiffness and high precision is established. Based on the optimization results, a compliant rotational joint with bidirectional anti-buckling, constant rotational stiffness, and high precision is designed. Finally, the effectiveness of the optimization method is validated through physical experiments.