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Existing CNNs-based salient object detection (SOD) heavily depends on the large-scale pixel-level annotations, which is labor-intensive, time-consuming, and expensive. By contrast, the sparse annotations become appealing to the salient object detection community. However, few efforts are devoted to learning salient object detection from sparse annotations, especially in the remote sensing field. In addition, the sparse annotation usually contains scanty information, which makes it challenging to train a well-performing model, resulting in its performance largely lagging behind the fully-supervised models. Although some SOD methods adopt some prior cues to improve the detection performance, they usually lack targeted discrimination of object boundaries and thus provide saliency maps with poor boundary localization. To this end, in this paper, we propose a novel weakly-supervised salient object detection framework to predict the saliency of remote sensing images from sparse scribble annotations. To implement it, we first construct the scribble-based remote sensing saliency dataset by relabelling an existing large-scale SOD dataset with scribbles, namely S-EOR dataset. After that, we present a novel scribble-based boundary-aware network (SBA-Net) for remote sensing salient object detection. Specifically, we design a boundary-aware module (BAM) to explore the object boundary semantics, which is explicitly supervised by the high-confidence object boundary (pseudo) labels generated by the boundary label generation (BLG) module, forcing the model to learn features that highlight the object structure and thus boosting the boundary localization of objects. Then, the boundary semantics are integrated with high-level features to guide the salient object detection under the supervision of scribble labels.