Large Language Models (LLMs) have recently demonstrated remarkable reasoning abilities, yet hallucinate on knowledge-intensive tasks. Retrieval-augmented generation (RAG) mitigates this issue by grounding answers in external sources, e.g., knowledge graphs (KGs). However, existing KG-based RAG approaches rely on semantics-unaware path sampling and are weakly aligned with KG reasoning objectives, which limits further accuracy gains. They also feed retrieved paths directly into the reasoner without organizing them into answer-centered reasoning paths, hindering small LLMs' ability to leverage the retrieved knowledge. Furthermore, prior works predominantly rely on large LLMs (e.g., ChatGPT/GPT-4) or assume backbones above 7B parameters, leaving sub-7B models underexplored. We address this gap with RPO-RAG, the first KG-based RAG framework specifically designed for small LLMs, to the best of our knowledge. RPO-RAG introduces three key innovations: (1) a query-path semantic sampling strategy that provides informative supervisory signals; (2) a relation-aware preference optimization that aligns training with intermediate KG reasoning signals (e.g., relation); and (3) an answer-centered prompt design that organizes entities and reasoning paths in an interpretable format. Extensive experiments on two benchmark Knowledge Graph Question Answering (KGQA) datasets, WebQSP and CWQ, demonstrate that RPO-RAG effectively bridges the performance gap between small and large language models. On WebQSP, it improves F1 by up to 8.8%, reflecting enhanced answer precision, while on CWQ it achieves new state-of-the-art results among models under 8B parameters in both Hit and F1. Overall, RPO-RAG substantially improves the reasoning capability of small LLMs, even under 3B parameters-highlighting their potential for resource-efficient and practical on-device KGQA applications.