Generating step-by-step "chain-of-thought" rationales has proven effective for improving the performance of large language models on complex reasoning tasks. However, applying such techniques to structured tasks, such as text-to-SQL, remains largely unexplored. In this paper, we introduce Self-Taught Reasoner for text-to-SQL (STaR-SQL), a novel approach that reframes SQL query generation as a reasoning-driven process. Our method prompts the LLM to produce detailed reasoning steps for SQL queries and fine-tunes it on rationales that lead to correct outcomes. Unlike traditional methods, STaR-SQL dedicates additional test-time computation to reasoning, thereby positioning LLMs as spontaneous reasoners rather than mere prompt-based agents. To further scale the inference process, we incorporate an outcome-supervised reward model (ORM) as a verifier, which enhances SQL query accuracy. Experimental results on the challenging Spider benchmark demonstrate that STaR-SQL significantly improves text-to-SQL performance, achieving an execution accuracy of 86.6%. This surpasses a few-shot baseline by 31.6% and a baseline fine-tuned to predict answers directly by 18.0%. Additionally, STaR-SQL outperforms agent-like prompting methods that leverage more powerful yet closed-source models such as GPT-4. These findings underscore the potential of reasoning-augmented training for structured tasks and open the door to extending self-improving reasoning models to text-to-SQL generation and beyond.