Generative artificial intelligence (GenAI) chatbots powered by large language models (LLMs) are increasingly used in health research to support a range of academic and clinical activities. While increasingly adopted in biomedical research, their application in traditional, complementary, and integrative medicine (TCIM) remains underexplored. TCIM presents unique challenges, including complex interventions, culturally embedded practices, and variable terminology. This article provides a practical, evidence-informed guide to help TCIM researchers engage responsibly with GenAI chatbots through prompt engineering, the design of clear, structured, and purposeful prompts to improve output relevance and accuracy. The guide outlines strategies to tailor GenAI chatbot interactions to the methodological and epistemological diversity of TCIM. It presents use cases across the research process, including research question development, study design, literature searches, selection of reporting guidelines and appraisal tools, quantitative and qualitative analysis, writing and dissemination, and implementation planning. For each stage, the guide offers examples and best practices while emphasizing that AI-generated content should always serve as a starting point, not a final product, and must be reviewed and verified using credible sources. Potential risks such as hallucinated outputs, embedded bias, and ethical challenges are discussed, particularly in culturally sensitive contexts. Transparency in GenAI chatbot use and researcher accountability are emphasized as essential principles. While GenAI chatbots can expand access to research support and foster innovation in TCIM, they cannot substitute for critical thinking, methodological rigour, or domain-specific expertise. Used responsibly, GenAI chatbots can augment human judgment and contribute meaningfully to the evolution of TCIM scholarship.