This study presents an advanced method for selecting anchoring positions for ships riding to a single anchor, with a focus on safety, feasibility, and optimization in the context of autonomous ship navigation. Grounded in nautical practice, the research defines the criteria for identifying safe anchorage waters and determining the appropriate anchor chain length to ensure secure mooring. The proposed method employs a gridding technique to systematically analyze the anchorage area, enabling a comprehensive search for feasible anchoring positions while accounting for environmental conditions and vessel dynamics. An optimal selection algorithm is integrated into the process to enhance decision-making in autonomous anchoring. Simulation experiments validate the effectiveness of the approach across various scenarios, demonstrating its robustness and practical applicability. The findings contribute to improved safety and efficiency in autonomous anchoring operations. The paper concludes with a critical discussion of the results, implications for autonomous maritime operations, and suggestions for future research.