The potential of large language models (LLMs) to mitigate the time- and cost-related challenges associated with inductive thematic analysis (ITA) is being increasingly explored in the literature. However, the use of LLMs to support ITA has often been opportunistic, relying on ad hoc prompt engineering (PE) approaches, thereby undermining the reliability, transparency, and replicability of the analysis. The goal of this study is to develop a structured approach to PE in LLM-assisted ITA. To this end, a comprehensive review of the existing literature is conducted to examine how researchers applying ITA integrate LLMs into their workflows and, in particular, how PE is utilized to support the analytical process. Built on the insights generated from this review, four key steps for effective PE in LLM-assisted ITA are identified and proposed. Furthermore, the study explores advanced PE techniques that can enhance the execution of these steps, providing researchers with practical strategies to improve their analyses. In conclusion, the main contributions of this paper include: (i) mapping the existing research on LLM-assisted ITA to enable a better understanding of the rapidly developing field, (ii) proposing a structured four-step PE process to enhance methodological rigor, (iii) discussing the application of advanced PE techniques to support the execution of these steps, and (iv) highlighting key directions for future research.