Finding appropriate prompts for the specific task has become an important issue as the usage of Large Language Models (LLM) have expanded. However, the variety of input-output formats complicate finding the prompts. Reinforcement Learning (RL) is a promising for prompt tuning due to its ability to incrementally produce better results through interaction with the environment. But its inherent training instability and environmental dependency make it difficult to use in practice. In this paper, we propose StablePrompt, a prompt tuning method based on RL. We formulate prompt tuning as RL problem between agent and target LLM, and introduce Adaptive Proximal Policy Optimization (APPO), an modified version of PPO for prompt tuning. APPO introduces an anchor model and updates it adaptively based on the training trajectory. Using this anchor model for the KL divergence term in PPO keeps the search space flexible and ensures training stability. We evaluate StablePrompt on various tasks, including text classification, question answering, and text generation. StablePrompt achieves State-of-The-Art performance across diverse tasks. We demonstrates that StablePrompt performs well across various types and sizes of LLMs. Furthermore, we present TTE-StablePrompt, an extension for generating input-dependent prompts. It outperforms StablePrompt in tasks that are hard to solve with a single prompt. This shows that StablePrompt is an extensible and stable RL framework for LLM.