Adhesion-based space climbing robots, with their flexibility and multi-functional capabilities, are seen as a promising candidate for in-orbit maintenance. However, challenges such as uncertain adhesion establishment, unexpected detachment, and body motion unsteadiness in microgravity environments persist. To address these issues, this paper proposes a coordinated force–position compliance control method that integrates novel adhesion establishment and rotational detachment strategies, integrated into the gait schedule for a space climbing robot. By monitoring the foot-end reaction forces in real time, the proposed method establishes adhesion without risking damaging the spacecraft exterior, and smooth detachment is achieved by rotating the foot joint instead of direct pulling. These strategies are dedicated to reducing unnecessary control actions and, accordingly, the required adhesion forces in all feet, reducing the possibility of unexpected detachment. Climbing experiments have been conducted in a suspension-based gravity compensation system to examine the merits of the proposed method. The experimental results demonstrate that the proposed rotational detaching method decreases the required pulling force by 65.5% compared to direct pulling, thus greatly reducing the disturbance introduced to the robot body and other supporting legs. When stepping on an obstacle, the compliant control method is shown to reduce unnecessarily aggressive control actions and result in a reduction in relevant normal and shear adhesion forces in the supporting legs by 44.8% and 35.1%, respectively, compared to a PID controller.