Recent studies have shown that disentanglement of classification and localization tasks has great potential to improve the performance of general object detection. However, such kind of disentanglement strategies remain not well explored in oriented object detection. Particularly, there exist two challenges lying in task disentanglement for oriented object detection: (1) existing task-decoupled methods ignore the orientation of objects, hardly coping with arbitrarily oriented objects; (2) the targets in oriented object detection (e.g., high-resolution remote sensing images) are generally small-size and fine-grained, making classification more difficult. To handle the above issues, we rethink task-decoupled policy in oriented object detection and propose an effective Orientation-aware Task-Decoupled Learning (OTDL) method. Specifically, our OTDL first presents a light-weight Task-specific Proposal Offset Learning (TPOL) module to generate the eligible proposals for arbitrarily oriented objects, where TPOL module equips classification and localization tasks with individual proposals by learning task-specific and orientation-aware offsets in a local coordinate. Furthermore, we empirically study the effect of various double-head strategies on performance of oriented object detection, while proposing a novel Pyramid Covariance Attention (PCA)-based classification head to cope with small-size and fine-grained targets. Based on the proposed TPOL module and PCA-based classification head, our OTDL explores the potential of task disentanglement for improving the performance of oriented object detection. The experiments are conducted on five oriented object detection benchmarks (i.e., DOTA-v1.0, DOTA-v1.5, HRSC2016, DIOR-R and SODA-A), and the results show our OTDL method significantly outperforms its counterparts, while achieving state-of-the-art performance.