The registration of bridge point cloud data (PCD) is an important preprocessing step for tasks such as bridge modeling, deformation detection, and bridge health monitoring. However, most existing research on bridge PCD registration only focused on pairwise registration, and payed insufficient attention to multi-view registration. In addition, to recover the overlaps of unordered multiple scans and obtain the merging order, extensive pairwise matching and the creation of a fully connected graph of all scans are often required, resulting in low efficiency. To address these issues, this paper proposes a marker-free template-guided method to align multiple unordered bridge PCD to a global coordinate system. Firstly, by aligning each scan to a given registration template, the overlaps between all the scans are recovered. Secondly, a fully connected graph is created based on the overlaps and scanning locations, and then a graph-partition algorithm is utilized to construct the scan-blocks. Then, the coarse-to-fine registration is performed within each scan-block, and the transformation matrix of coarse registration is obtained using an intelligent optimization algorithm. Finally, global block-to-block registration is performed to align all scans to a unified coordinate reference system. We tested our framework on different bridge point cloud datasets, including a suspension bridge and a continuous rigid frame bridge, to evaluate its accuracy. Experimental results demonstrate that our method has high accuracy.