Schema linking is a critical step in Text-to-SQL task, aiming to accurately predict the table names and column names required for the SQL query based on the given question. However, current fine-tuning approaches for schema linking models employ a rote-learning paradigm, excessively optimizing for ground truth schema linking outcomes while compromising reasoning ability. This limitation arises because of the difficulty in acquiring a high-quality reasoning sample for downstream tasks. To address this, we propose Schema-R1, a reasoning schema linking model trained using reinforcement learning. Specifically, Schema-R1 consists of three key steps: constructing small batches of high-quality reasoning samples, supervised fine-tuning for cold-start initialization, and rule-based reinforcement learning training. The final results demonstrate that our method effectively enhances the reasoning ability of the schema linking model, achieving a 10\% improvement in filter accuracy compared to the existing method. Our code is available at https://github.com/hongWin/Schema-R1/.