Recent research in zero-shot Relation Extraction (RE) has focused on using Large Language Models (LLMs) due to their impressive zero-shot capabilities. However, current methods often perform suboptimally, mainly due to a lack of detailed, context-specific prompts needed for understanding various sentences and relations. To address this, we introduce the Self-Prompting framework, a novel method designed to fully harness the embedded RE knowledge within LLMs. Specifically, our framework employs a three-stage diversity approach to prompt LLMs, generating multiple synthetic samples that encapsulate specific relations from scratch. These generated samples act as in-context learning samples, offering explicit and context-specific guidance to efficiently prompt LLMs for RE. Experimental evaluations on benchmark datasets show our approach outperforms existing LLM-based zero-shot RE methods. Additionally, our experiments confirm the effectiveness of our generation pipeline in producing high-quality synthetic data that enhances performance.