In view of the limited precision of traditional point cloud registration methods in bridge engineering, as well as the lack of intuitive guidance for bridge construction control regarding relative coordinate relationships of point clouds, this study proposes a novel dual-purpose target for the total station and laser scanner, along with a corresponding algorithm. The scanning point cloud undergoes intensity filtering, clustering, planar denoising, contour extraction, centroid fitting, registration transformation, target recognition, registration, and coordinate transformation. Experimental results demonstrate that the proposed algorithm can accurately extract the centroid coordinates of the targets and effectively handle complex on-site conditions. The coordinate transformation achieves high precision, with an amplification error of only 2.1 mm at a distance of 500 m. The registration precision between planar and spherical targets is nearly identical, surpassing that of planar iterative and ICP algorithms. Application of the algorithm in the context of China’s large double-span steel-tube concrete arch bridge scenario. it was found that the maximum deviation of the radius of the main chord tube was 10.8 mm, the maximum deviation of the distance from the center of the main chord tube was 8.3 mm, the average length of the merging opening was 775.0 mm, the maximum lateral deviation of the merging opening was 9.6 mm, and the maximum deviation of the height of merging opening was 25.2 mm. The results showed that no additional restraining measures were needed, and the smooth jointing could be realized only under a suitable temperature. Comparison with measurements obtained from the TS60 total station exhibits a close match, with a verification error within 3.9 mm, thereby meeting the precision requirements for construction control.