Recently, Large Language Models (LLMs) have shown strong potential in recommendation tasks due to their broad world knowledge and reasoning capabilities. However, applying them to serendipity-oriented recommendation remains challenging, mainly due to a domain gap of LLMs in modeling personalized user behavior and the scarcity of labeled serendipitous interactions. In this paper, we introduce **SOLAR** (**S**erendipity-**O**ptimized **L**anguage model **A**ligned for **R**ecommendation), a two-stage framework that addresses these challenges. To alleviate label scarcity, we adopt a weak supervision strategy: a sequential ID-based recommender generates candidate items, which are then reranked by an LLM acting as a preference judge to produce serendipity-aware pseudo-labels. To bridge the domain gap, we propose a domain-adaptive instruction tuning method (SUN) that aligns LLMs with recommendation tasks. Experiments on three real-world datasets show that **SOLAR** consistently improves both accuracy and serendipity over strong baselines, showing its effectiveness in enabling more diverse, user-centric recommendations. Code and dataset are released at [https://github.com/SOLAR2025ARR/SOLAR](https://github.com/SOLAR2025ARR/SOLAR).