The proliferation of rumors on social networks undermines information credibility. While their dissemination forms complex networks, current detection methods struggle to capture these intricate propagation patterns. Representing each node solely through its textual embeddings neglects the textual coherence across the entire rumor propagation path, which compromises the accuracy of rumor identification on social platforms. We propose a novel framework that leverages Large Language Models (LLMs) to address these limitations. Our approach captures subtle rumor signals by employing LLMs to analyze information subchains, assign rumor probabilities and intelligently construct connections to virtual nodes. This enables the modification of the original graph structure, which is a critical advancement for capturing subtle rumor signals. Given the inherent limitations of LLMs in rumor identification, we develop a structured prompt framework to mitigate model biases and ensure robust graph learning performance. Additionally, the proposed framework is model-agnostic, meaning it is not constrained to any specific graph learning algorithm or LLMs. Its plug-and-play nature allows for seamless integration with further fine-tuned LLMs and graph techniques in the future, potentially enhancing predictive performance without modifying original algorithms.