Traditional information retrieval (IR) methods excel at textual and semantic matching but struggle in reasoning-intensive retrieval tasks that require multi-hop inference or complex semantic understanding between queries and documents. One promising solution is to explicitly rewrite or augment queries using large language models (LLMs) to elicit reasoning-relevant content prior to retrieval. However, the widespread use of large-scale LLMs like GPT-4 or LLaMA3-70B remains impractical due to their high inference cost and limited deployability in real-world systems. In this work, we introduce Reinforced Query Reasoner (RQR), a family of small-scale language models for query reasoning and rewriting in reasoning-intensive retrieval. Our approach frames query reformulation as a reinforcement learning problem and employs a novel semi-rule-based reward function. This enables smaller language models, e.g., Qwen2.5-7B-Instruct and Qwen2.5-1.5B-Instruct, to achieve reasoning performance rivaling large-scale LLMs without their prohibitive inference costs. Experiment results on BRIGHT benchmark show that, with BM25 as retrievers, both RQR-7B and RQR-1.5B models significantly outperform existing baselines, including prompt-based query reasoners and some latest dense retrievers trained for reasoning-intensive retrieval tasks, offering superior adaptability for real-world deployment. All code and dataset will be publicly released.