The melting of Arctic ice has increased the value of Arctic shipping, making research on the Arctic route a popular topic. However, ships navigating this route will likely encounter randomly distributed sea ice, which poses significant safety hazards to local path planning. The Dynamic Window Approach (DWA) is a suitable method for local path planning, but the DWA results in large ship rotation angles, increasing navigation risk. This study proposes a novel fuzzy control path planning algorithm based on scale factors to address this issue. The proposed algorithm combines a stability fuzzy controller with a collision risk controller to carry out adaptive control of DWA. Two scale factors are defined to improve fuzzy control based on the overall and obstacle avoidance phases. Results show that the proposed algorithm significantly reduces the rotation angle of DWA, improves the effect by 19.52%, shortens distance and time, and increases safety when encountering sea ice.