Collectible card games (CCGs) are a difficult genre for AI due to their partial observability, long-term decision-making, and evolving card sets. Due to this, current AI models perform vastly worse than human players at CCG tasks such as deckbuilding and gameplay. In this work, we introduce UrzaGPT, a domain-adapted large language model that recommends real-time drafting decisions in Magic: The Gathering. Starting from an open-weight LLM, we use Low-Rank Adaptation fine-tuning on a dataset of annotated draft logs. With this, we leverage the language modeling capabilities of LLM, and can quickly adapt to different expansions of the game. We benchmark UrzaGPT in comparison to zero-shot LLMs and the state-of-the-art domain-specific model. Untuned, small LLMs like Llama-3-8B are completely unable to draft, but the larger GPT-4o achieves a zero-shot performance of 43%. Using UrzaGPT to fine-tune smaller models, we achieve an accuracy of 66.2% using only 10,000 steps. Despite this not reaching the capability of domain-specific models, we show that solely using LLMs to draft is possible and conclude that using LLMs can enable performant, general, and update-friendly drafting AIs in the future.