Reducing the annotation cost of oriented object detection in remote sensing remains a major challenge. Recently, sparse annotation has gained attention for effectively reducing annotation redundancy in densely remote sensing scenes. However, (1) the sparse data reliance on class-dependent sampling, and (2) the lack of in-depth investigation into the characteristics of sparse samples hinders its further development. This paper proposes an active learning-based sparsely annotated oriented object detection (SAOOD) method, termed Active-SAOOD. Based on a model state observation module, Active-SAOOD actively selects the most valuable sparse samples at the instance level that are best suited to the current model state, by jointly considering orientation, classification, and localization uncertainty, as well as inter- and intra-class diversity. This design enables SAOOD to operate stably under completely randomly initialized sparse annotations and extends its applicability to broader real-world. Experiments on multiple datasets demonstrate that Active-SAOOD significantly improves both performance and stability of existing SAOOD methods under various random sparse annotation. In particular, with only 1\% annotated ratios, it achieves a 9\% performance gain over the baseline, further enhancing the practical value of SAOOD in remote sensing. The code will be public.