In the vehicle pose estimation task based on roadside Lidar in cooperative perception, the measurement distance, angle, and laser resolution directly affect the quality of the target point cloud. For incomplete and sparse point clouds, current methods are either less accurate in correspondences solved by local descriptors or not robust enough due to the reduction of effective boundary points. In response to the above weakness, this paper proposed a registration algorithm Environment Constraint Principal Component-Iterative Closest Point (ECPC-ICP), which integrated road information constraints. The road normal feature was extracted, and the principal component of the vehicle point cloud matrix under the road normal constraint was calculated as the initial pose result. Then, an accurate 6D pose was obtained through point-to-point ICP registration. According to the measurement characteristics of the roadside Lidars, this paper defined the point cloud sparseness description. The existing algorithms were tested on point cloud data with different sparseness. The simulated experimental results showed that the positioning MAE of ECPC-ICP was about 0.5% of the vehicle scale, the orientation MAE was about 0.26°, and the average registration success rate was 95.5%, which demonstrated an improvement in accuracy and robustness compared with current methods. In the real test environment, the positioning MAE was about 2.6% of the vehicle scale, and the average time cost was 53.19 ms, proving the accuracy and effectiveness of ECPC-ICP in practical applications.