Effective personalized question answering (PQA) in language models requires grounding responses in the user's underlying intent, where intent refers to the implicit ``why'' behind a query beyond its explicit wording. However, existing approaches to intent-aware personalization rely on multi-turn conversational context or rich user profiles, and do not explicitly model user intent during the reasoning process. This limits their effectiveness in single-turn settings, where the user's latent goal must be inferred from minimal input and integrated into the thinking and reasoning process. To bridge this gap, we propose IAP (Intent-Aware Personalization), a reinforcement learning framework that trains models to infer implicit user intent directly from a single-turn question and incorporate it into thinking steps through a tag-based schema for generating personalized, intent-grounded answers. By optimizing intent-aware answer trajectories under a personalized reward function, IAP reinforces generation paths that make implicit user intent explicit and produce responses that better align with the user's underlying goal. Through experiments on the LaMP-QA benchmark across six models, IAP consistently outperforms all baselines, achieving an average macro-score gain of around 7.5\% over the strongest competitor, demonstrating that modeling implicit user intent within the training objective is a promising direction for PQA.