Cross-domain recommendation (CDR) has emerged as a promising solution to the cold-start problem, faced by single-domain recommender systems. However, existing CDR models rely on complex neural architectures, large datasets, and significant computational resources, making them less effective in data-scarce scenarios or when simplicity is crucial. In this work, we leverage the reasoning capabilities of large language models (LLMs) and explore their performance in the CDR domain across multiple domain pairs. We introduce two novel prompt designs tailored for CDR and demonstrate that LLMs, when prompted effectively, outperform state-of-the-art CDR baselines across various metrics and domain combinations in the rating prediction and ranking tasks. This work bridges the gap between LLMs and recommendation systems, showcasing their potential as effective cross-domain recommenders.