Referring Remote Sensing Image Segmentation (RRSIS) is a new challenge that combines computer vision and natural language processing, delineating specific regions in aerial images as described by textual queries. Traditional Referring Image Segmentation (RIS) approaches have been impeded by the complex spatial scales and orientations found in aerial imagery, leading to suboptimal segmentation results. To address these challenges, we introduce the Rotated Multi-Scale Interaction Network (RMSIN), an innovative approach designed for the unique demands of RRSIS. RMSIN incorporates an Intra-scale Interaction Module (IIM) to effectively address the fine-grained detail required at multiple scales and a Cross-scale Interaction Module (CIM) for integrating these details coherently across the network. Furthermore, RMSIN employs an Adaptive Rotated Convolution (ARC) to account for the diverse orientations of objects, a novel contribution that significantly enhances segmentation accuracy. To assess the efficacy of RMSIN, we have curated an expansive dataset comprising 17,402 image-caption-mask triplets, which is unparalleled in terms of scale and variety. This dataset not only presents the model with a wide range of spatial and rotational scenarios but also establishes a stringent benchmark for the RRSIS task, ensuring a rigorous evaluation of performance. Our experimental evaluations demonstrate the exceptional performance of RMSIN, surpassing existing state-of-the-art models by a significant margin. All datasets and code will be made available.