Introducing Point-TTA, a new framework for point cloud registration (PCR) that enhances the performance and generalization of registration models. Despite the impressive progress made by learning-based methods, adapting to unknown testing environments remains a challenge due to variations in 3D scans. Current methods typically train a generic model and apply it to all instances during testing, which may not be optimal for handling the diverse variations. In this study, we propose a test-time adaptation approach for PCR that enables our model to adapt to unseen distributions at test-time without prior knowledge of the test data. We achieve this by designing three self-supervised auxiliary tasks that are optimized alongside the primary PCR task. When presented with a test instance, our model adapts using these auxiliary tasks, and the updated model is then used for inference. During training, our model is trained using a meta-auxiliary learning approach, ensuring that the adapted model via auxiliary tasks improves the accuracy of the primary task. Experimental results indicate that our approach effectively improves generalization in point cloud registration and outperforms other state-of-the-art methods.