Large language models (LLMs) have demonstrated exceptional performance across a wide variety of domains. Nonetheless, generalist LLMs continue to fall short in reasoning tasks necessitating specialized knowledge. Prior investigations into specialized LLMs focused on domain-specific training, which entails substantial efforts in domain data acquisition and model parameter fine-tuning. To address these challenges, this paper proposes the Way-to-Specialist (WTS) framework, which synergizes retrieval-augmented generation with knowledge graphs (KGs) to enhance the specialized capability of LLMs in the absence of specialized training. In distinction to existing paradigms that merely utilize external knowledge from general KGs or static domain KGs to prompt LLM for enhanced domain-specific reasoning, WTS proposes an innovative "LLM$\circlearrowright$KG" paradigm, which achieves bidirectional enhancement between specialized LLM and domain knowledge graph (DKG). The proposed paradigm encompasses two closely coupled components: the DKG-Augmented LLM and the LLM-Assisted DKG Evolution. The former retrieves question-relevant domain knowledge from DKG and uses it to prompt LLM to enhance the reasoning capability for domain-specific tasks; the latter leverages LLM to generate new domain knowledge from processed tasks and use it to evolve DKG. WTS closes the loop between DKG-Augmented LLM and LLM-Assisted DKG Evolution, enabling continuous improvement in the domain specialization as it progressively answers and learns from domain-specific questions. We validate the performance of WTS on 6 datasets spanning 5 domains. The experimental results show that WTS surpasses the previous SOTA in 4 specialized domains and achieves a maximum performance improvement of 11.3%.