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In recent years, LiDAR sensors have become pervasive in the solutions to localization tasks for autonomous systems. One key step in using LiDAR data for localization is the alignment of two LiDAR scans taken from different poses, a process called scan-matching or point cloud registration. Most existing algorithms for this problem are heuristic in nature and local, meaning they may not produce accurate results under poor initialization. Moreover, existing methods give no guarantee on the quality of their output, which can be detrimental for safety-critical tasks. In this paper, we analyze a simple algorithm for point cloud registration, termed PASTA. This algorithm is global and does not rely on point-to-point correspondences, which are typically absent in LiDAR data. Moreover, and to the best of our knowledge, we offer the first point cloud registration algorithm with provable error bounds. Finally, we illustrate the proposed algorithm and error bounds in simulation on a simple trajectory tracking task.