Image-to-point-cloud registration (I2P) is a fundamental task in robotic applications such as manipulation,grasping, and localization. Existing deep learning-based I2P methods seek to align image and point cloud features in a learned representation space to establish correspondences, and have achieved promising results. However, when the inlier ratio of the initial matching pairs is low, conventional Perspective-n-Points (PnP) methods may struggle to achieve accurate results. To address this limitation, we propose Angle-I2P, an outlier rejection network that leverages angle-consistent geometric constraints and hierarchical attention. First, we design a scale-invariant, crossmodality geometric constraint based on angular consistency. This explicit geometric constraint guides the model in distinguishing inliers from outliers. Furthermore, we propose a global-tolocal hierarchical attention mechanism that effectively filters out geometrically inconsistent matches under rigid transformation, thereby improving the Inlier Ratio (IR) and Registration Recall (RR). Experimental results demonstrate that our method achieves state-of-the-art performance on the 7Scenes, RGBD Scenes V2, and a self-collected dataset, with consistent improvements across all benchmarks.