Prompt-tuning has received attention as an efficient tuning method in the language domain, i.e., tuning a prompt that is a few tokens long, while keeping the large language model frozen, yet achieving comparable performance with conventional fine-tuning. Considering the emerging privacy concerns with language models, we initiate the study of privacy leakage in the setting of prompt-tuning. We first describe a real-world email service pipeline to provide customized output for various users via prompt-tuning. Then we propose a novel privacy attack framework to infer users' private information by exploiting the prompt module with user-specific signals. We conduct a comprehensive privacy evaluation on the target pipeline to demonstrate the potential leakage from prompt-tuning. The results also demonstrate the effectiveness of the proposed attack.