Interpreting figurative language such as sarcasm across multi-modal inputs presents unique challenges, often requiring task-specific fine-tuning and extensive reasoning steps. However, current Chain-of-Thought approaches do not efficiently leverage the same cognitive processes that enable humans to identify sarcasm. We present IRONIC, an in-context learning framework that leverages Multi-modal Coherence Relations to analyze referential, analogical and pragmatic image-text linkages. Our experiments show that IRONIC achieves state-of-the-art performance on zero-shot Multi-modal Sarcasm Detection across different baselines. This demonstrates the need for incorporating linguistic and cognitive insights into the design of multi-modal reasoning strategies. Our code is available at: https://github.com/aashish2000/IRONIC