The rotation robustness property has drawn much attention to point cloud analysis, whereas it still poses a critical challenge in 3D object detection. When subjected to arbitrary rotation, most existing detectors fail to produce expected outputs due to the poor rotation robustness. In this paper, we present RIDE, a pioneering exploration of Rotation-Invariance for the 3D LiDAR-point-based object DEtector, with the key idea of designing rotation-invariant features from LiDAR scenes and then effectively incorporating them into existing 3D detectors. Specifically, we design a bi-feature extractor that extracts (i) object-aware features though sensitive to rotation but preserve geometry well, and (ii) rotation-invariant features, which lose geometric information to a certain extent but are robust to rotation. These two kinds of features complement each other to decode 3D proposals that are robust to arbitrary rotations. Particularly, our RIDE is compatible and easy to plug into the existing one-stage and two-stage 3D detectors, and boosts both detection performance and rotation robustness. Extensive experiments on the standard benchmarks showcase that the mean average precision (mAP) and rotation robustness can be significantly boosted by integrating with our RIDE, with +5.6% mAP and 53% rotation robustness improvement on KITTI, +5.1% and 28% improvement correspondingly on nuScenes. The code will be available soon.