Embodied agents must perform reference resolution if they are to achieve sufficient language understanding with humans. But situated interaction introduces social norms, which are often overlooked yet critically need to be reasoned together with language to resolve references. To address this issue, we offer a novel normative-based reasoning approach to reference resolution and provide a proof-of-concept implementation in a cognitive robotic architecture with natural language human-robot interaction capabilities. We discuss reference resolution problems that require different levels of normative reasoning, demonstrate how a large language model, GPT-3, struggles to consistently identify target referents when normative reasoning is needed, provide a user study to show how humans perform norm-guided reference resolution, and demonstrate the successful operation of our proposed architecture on a fully autonomous assistive robot interacting with human instructors in natural language.