To address the limitations of the RRT* algorithm in robotic manipulator path planning, particularly in planning efficiency, path quality, and obstacle avoidance capability in complex environments, this paper proposed a Tangential Dynamic Artificial Potential Field-RRT* (TDAPF-RRT*) algorithm, which integrated an improved artificial potential field with a bidirectional RRT* framework. First, TDAPF-RRT* constructed an adaptive 3D sampling box based on the start and goal points. Then, the algorithm introduced a density-aware rejection mechanism to suppress local redundant sampling and improve the quality of sampling points. Based on a sliding window, the algorithm calculated the failure rate of recent target-biased expansions and adaptively adjusted the target-bias probability to accelerate convergence. The algorithm enhanced both the attractive and repulsive forces and introduced a tangential force, so that the resultant force repelled obstacles while providing tangential sliding guidance along feasible paths, thereby improving the robot’s ability to navigate around obstacles stably in complex environments. Finally, the algorithm pruned the generated raw path and applied a cubic B-spline curve for smoothing, thereby improving the continuity and stability of robotic manipulator motion. Simulation results in complex environments demonstrate that, compared with the RRT* algorithm, TDAPF-RRT* reduces the path length by 13.10%, decreases the average number of nodes by 86.22%, shortens the path planning runtime by 88.11%, and reduces the average path turning angle by 31.29%. Experimental results on the Elite EC612 robotic manipulator platform further show that, relative to the RRT* algorithm, TDAPF-RRT* reduces the total runtime for completing full path planning by 50.04%, thereby verifying its effectiveness and feasibility.