Text in natural images is of arbitrary orientations, requiring detection in terms of oriented bounding boxes. Normally, a multi-oriented text detector often involves two key tasks: 1) text presence detection, which is a classification problem disregarding text orientation; 2) oriented bounding box regression, which concerns about text orientation. Previous methods rely on shared features for both tasks, resulting in degraded performance due to the incompatibility of the two tasks. To address this issue, we propose to perform classification and regression on features of different characteristics, extracted by two network branches of different designs. Concretely, the regression branch extracts rotation-sensitive features by actively rotating the convolutional filters, while the classification branch extracts rotation-invariant features by pooling the rotation-sensitive features. The proposed method named Rotation-sensitive Regression Detector (RRD) achieves state-of-the-art performance on three oriented scene text benchmark datasets, including ICDAR 2015, MSRA-TD500, RCTW-17 and COCO-Text. Furthermore, RRD achieves a significant improvement on a ship collection dataset, demonstrating its generality on oriented object detection.