Taxonomies are hierarchical classifications widely exploited to facilitate downstream natural language processing tasks. The taxonomy expansion task aims to incorporate emergent concepts into the existing taxonomies. Prior works focus on modeling the local substructure of taxonomies but neglect the global structure. In this paper, we propose TaxoPrompt, a framework that learns the global structure by prompt tuning with taxonomic context. Prompt tuning leverages a template to formulate downstream tasks into masked language model form for better distributed semantic knowledge use. To further infuse global structure knowledge into language models, we enhance the prompt template by exploiting the taxonomic context constructed by a variant of the random walk algorithm. Experiments on seven public benchmarks show that our proposed TaxoPrompt is effective and efficient in automatically expanding taxonomies and achieves state-of-the-art performance.