Tabular prediction has traditionally relied on gradient-boosted decision trees and specialized deep learning models, which excel within tasks but provide limited interpretability and weak transfer across tables. Reasoning large language models (LLMs) promise cross-task adaptability with trans- parent reasoning traces, yet their potential has not been fully realized for tabular data. This paper presents TabR1, the first reasoning LLM for tabular prediction with multi-step reasoning. At its core is Permutation Relative Policy Optimization (PRPO), a simple yet efficient reinforcement learning method that encodes column-permutation invariance as a structural prior. By construct- ing multiple label-preserving permutations per sample and estimating advantages both within and across permutations, PRPO transforms sparse rewards into dense learning signals and improves generalization. With limited supervision, PRPO activates the reasoning ability of LLMs for tabular prediction, enhancing few-shot and zero-shot performance as well as interpretability. Comprehensive experiments demonstrate that TabR1 achieves performance comparable to strong baselines under full-supervision fine-tuning. In the zero-shot setting, TabR1 approaches the performance of strong baselines under the 32-shot setting. Moreover, TabR1 (8B) substantially outperforms much larger LLMs across various tasks, achieving up to 53.17% improvement over DeepSeek-R1 (685B).

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