As the market for illicit drugs remains extremely profitable, major online platforms have become direct-to-consumer intermediaries for illicit drug trafficking participants. These online activities raise significant social concerns that require immediate actions. Existing approaches to combat this challenge are generally impractical due to the scarcity of labeled samples and imbalance of classes in real-world applications. To this end, we propose a novel Large Language Model-empowered Heterogeneous Graph Prompt Learning framework for illicit Drug Trafficking detection, called LLM-HetGDT that leverages LLM to facilitate heterogeneous graph neural networks (HGNNs) to effectively identify minority classes, i.e., drug trafficking participants, in the class-imbalanced scenarios. Specifically, we first pre-train HGNN over a contrastive pretext task to capture the inherent node and structure information over an unlabeled drug trafficking heterogeneous graph (HG). Afterward, to alleviate the class-imbalanced issue, we leverage LLMs to augment the HG by generating high-quality synthetic user nodes in the minority classes. Then, we fine-tune the soft prompts on the augmented HG to capture the important information in the minority classes for the downstream drug trafficking detection task. To comprehensively study online illicit drug trafficking activities, we collect a new HG dataset over Twitter, called Twitter-HetDrug. Extensive experiments on this dataset demonstrate the effectiveness, efficiency, and applicability of our proposed method by comparing it with state-of-the-art baseline methods. Our source code is available at https://github.com/GraphResearcher/LLM-HetGDT.