Text rewriting with differential privacy (DP) provides concrete theoretical guarantees for protecting the privacy of individuals in textual documents. In practice, existing systems may lack the means to validate their privacy-preserving claims, leading to problems of transparency and reproducibility. We introduce DP-Rewrite, an open-source framework for differentially private text rewriting which aims to solve these problems by being modular, extensible, and highly customizable. Our system incorporates a variety of downstream datasets, models, pre-training procedures, and evaluation metrics to provide a flexible way to lead and validate private text rewriting research. To demonstrate our software in practice, we provide a set of experiments as a case study on the ADePT DP text rewriting system, detecting a privacy leak in its pre-training approach. Our system is publicly available, and we hope that it will help the community to make DP text rewriting research more accessible and transparent.