E-commerce search engines often rely solely on product titles as input for ranking models with latency constraints. However, this approach can result in suboptimal relevance predictions, as product titles often lack sufficient detail to capture query intent. While product descriptions provide richer information, their verbosity and length make them unsuitable for real-time ranking, particularly for computationally expensive architectures like cross-encoder ranking models. To address this challenge, we propose ReLSum, a novel reinforcement learning framework designed to generate concise, query-relevant summaries of product descriptions optimized for search relevance. ReLSum leverages relevance scores as rewards to align the objectives of summarization and ranking, effectively overcoming limitations of prior methods, such as misaligned learning targets. The framework employs a trainable large language model (LLM) to produce summaries, which are then used as input for a cross-encoder ranking model. Experimental results demonstrate significant improvements in offline metrics, including recall and NDCG, as well as online user engagement metrics. ReLSum provides a scalable and efficient solution for enhancing search relevance in large-scale e-commerce systems.