Large language models (LLMs) have demonstrated remarkable advances in reasoning capabilities. However, their performance remains constrained by limited access to explicit and structured domain knowledge. Retrieval-Augmented Generation (RAG) addresses this by incorporating external information as context to augment reasoning. Nevertheless, traditional RAG systems typically operate over unstructured and fragmented text, resulting in low information density and suboptimal reasoning. To overcome these limitations, we propose \textsc{Structure-R1}, a novel framework that transforms retrieved content into structured representations optimized for reasoning. Leveraging reinforcement learning, \textsc{Structure-R1} learns a content representation policy that dynamically generates and adapts structural formats based on the demands of multi-step reasoning. Unlike prior methods that rely on fixed schemas, our approach adopts a generative paradigm capable of producing task-specific structures tailored to individual queries. To ensure the quality and reliability of these representations, we introduce a self-reward structural verification mechanism that checks whether the generated structures are both correct and self-contained. Extensive experiments on seven knowledge-intensive benchmarks show that \textsc{Structure-R1} consistently achieves competitive performance with a 7B-scale backbone model and matches the performance of much larger models. Additionally, our theoretical analysis demonstrates how structured representations enhance reasoning by improving information density and contextual clarity. Our code and data are available at: https://github.com/jlwu002/sr1.