Salient object detection (SOD) for optical remote sensing images (RSIs) aims at locating and extracting visually distinctive objects/regions from the optical RSIs. Despite some saliency models were proposed to solve the intrinsic problem of optical RSIs (such as complex background and scale-variant objects), the accuracy and completeness are still unsatisfactory. To this end, we propose a relational reasoning network with parallel multi-scale attention for SOD in optical RSIs in this paper. The relational reasoning module that integrates the spatial and the channel dimensions is designed to infer the semantic relationship by utilizing high-level encoder features, thereby promoting the generation of more complete detection results. The parallel multi-scale attention module is proposed to effectively restore the detail information and address the scale variation of salient objects by using the low-level features refined by multi-scale attention. Extensive experiments on two datasets demonstrate that our proposed RRNet outperforms the existing state-of-the-art SOD competitors both qualitatively and quantitatively.