Data containing personal information is increasingly used to train, fine-tune, or query Large Language Models (LLMs). Text is typically scrubbed of identifying information prior to use, often with tools such as Microsoft's Presidio or Anthropic's PII purifier. These tools have traditionally been evaluated on their ability to remove specific identifiers (e.g., names), yet their effectiveness at preventing re-identification remains unclear. We introduce RAT-Bench, a comprehensive benchmark for text anonymization tools based on re-identification risk. Using U.S. demographic statistics, we generate synthetic text containing various direct and indirect identifiers across domains, languages, and difficulty levels. We evaluate a range of NER- and LLM-based text anonymization tools and, based on the attributes an LLM-based attacker is able to correctly infer from the anonymized text, we report the risk of re-identification in the U.S. population, while properly accounting for the disparate impact of identifiers. We find that, while capabilities vary widely, even the best tools are far from perfect in particular when direct identifiers are not written in standard ways and when indirect identifiers enable re-identification. Overall we find LLM-based anonymizers, including new iterative anonymizers, to provide a better privacy-utility trade-off albeit at a higher computational cost. Importantly, we also find them to work well across languages. We conclude with recommendations for future anonymization tools and will release the benchmark and encourage community efforts to expand it, in particular to other geographies.