Text detoxification, a variant of style transfer tasks, finds useful applications in online social media. This work presents a fine-tuning method that only uses non-parallel data to turn large language models (LLM) into a detoxification rewritter. We model the fine-tuning process as a Stackelberg game between an LLM (leader) and a toxicity screener (follower), which is a binary style classifier (toxic or non-toxic). The LLM aims to align its preference according to the screener and generate paraphases passing the screening. The primary challenge of non-parallel data fine-tuning is incomplete preference. In the case of unsuccessful paraphrases, the classifier cannot establish a preference between the input and paraphrase, as they belong to the same toxic style. Hence, preference-alignment fine-tuning methods, such as direct preference optimization (DPO), no longer apply. To address the challenge of incomplete preference, we propose Stackelberg response optimization (SRO), adapted from DPO, to enable the LLM to learn from the follower's response. The gist is that SRO decreases the likelihood of generating the paraphrase if it fails the follower's screening while performing DPO on the pair of the toxic input and its paraphrase when the latter passes the screening. Experiments indicate that the SRO-fine-tunned LLM achieves satisfying performance comparable to state-of-the-art models regarding style accuracy, content similarity, and fluency. The overall detoxification performance surpasses other computing methods and matches the human reference. Additional empirical evidence suggests that SRO is sensitive to the screener's feedback, and a slight perturbation leads to a significant performance drop. We release the code and LLM models at \url{https://github.com/XXXinhong/Detoxification_LLM}.