To manage and optimize constantly evolving wireless networks, existing machine learning (ML)- based studies operate as black-box models, leading to increased computational costs during training and a lack of transparency in decision-making, which limits their practical applicability in wireless networks. Motivated by recent advancements in large language model (LLM)-enabled wireless networks, this paper proposes ProWin, a novel framework that leverages reinforced in-context learning to design task-specific demonstration Prompts for Wireless Network optimization, relying on the inference capabilities of LLMs without the need for dedicated model training or finetuning. The task-specific prompts are designed to incorporate natural language descriptions of the task description and formulation, enhancing interpretability and eliminating the need for specialized expertise in network optimization. We further propose a reinforced in-context learning scheme that incorporates a set of advisable examples into task-specific prompts, wherein informative examples capturing historical environment states and decisions are adaptively selected to guide current decision-making. Evaluations on a case study of base station power control showcases that the proposed ProWin outperforms reinforcement learning (RL)-based methods, highlighting the potential for next-generation future wireless network optimization.