Graph-based fraud detection has emerged as a crucial technique for identifying anomalous patterns and suspicious behaviors across various domains, including financial transactions, e-commerce, and cybersecurity. However, existing methods predominantly rely on substantial labeled data for training, limiting their effectiveness in real-world scenarios where labels are scarce. Leveraging the exceptional zero-shot reasoning and instruction-following capabilities of Large Language Models (LLMs), we propose FRAUDLLM: Fraud Reasoning and Anomaly Detection via Unified Design with Large Language Models, a novel zero-shot fraud detection framework. Specifically, it first generates semantic-rich text-graph pairs based on node metadata. Then, a pretrained text-graph aligner is employed to bridge the representation gap between the graph encoder and the text space of the LLM. Additionally, an in-context learning framework is designed to enable the LLM to effectively understand complex graph structures, significantly improving fraud detection performance in zero-shot scenarios without relying on labeled neighbor information. Extensive experiments on real-world datasets demonstrate that FRAUDLLM achieves state-of-the-art performance in zero-shot fraud detection tasks.