Object detection through either RGB images or the LiDAR point clouds has been extensively explored in autonomous driving. However, it remains challenging to make these two data sources complementary and beneficial to each other. In this paper, we propose \textit{AutoAlign}, an automatic feature fusion strategy for 3D object detection. Instead of establishing deterministic correspondence with camera projection matrix, we model the mapping relationship between the image and point clouds with a learnable alignment map. This map enables our model to automate the alignment of non-homogenous features in a dynamic and data-driven manner. Specifically, a cross-attention feature alignment module is devised to adaptively aggregate \textit{pixel-level} image features for each voxel. To enhance the semantic consistency during feature alignment, we also design a self-supervised cross-modal feature interaction module, through which the model can learn feature aggregation with \textit{instance-level} feature guidance. Extensive experimental results show that our approach can lead to 2.3 mAP and 7.0 mAP improvements on the KITTI and nuScenes datasets, respectively. Notably, our best model reaches 70.9 NDS on the nuScenes testing leaderboard, achieving competitive performance among various state-of-the-arts.