This paper introduces Wavelet-Induced Rotary Encodings (WIRE), an extension of Rotary Position Encodings (RoPE), a widely used algorithm in LLM and ViT, to graph-structured data. WIRE is more general than RoPE and demonstrates that it can recover RoPE in the special case of grid graphs. It also possesses desirable theoretical properties, such as isovariance under node reordering, compatibility with linear attention, and asymptotic dependence on graph-resistance distance under certain conditions. WIRE has been tested on a variety of synthetic and real-world tasks, including monochromatic subgraph identification, semantic segmentation of point clouds, and other standard graph benchmarks. It demonstrates effective performance in settings where graph structure is important.