We characterize how people are turning to LLMs as oracles: all-knowing authorities on subjective personal questions. Motivated by risks to users' autonomy and well-being, we develop a typology and LLM-based methods to measure this form of AI reliance at scale and understand how people are offloading judgment and decision-making to AI. Applying our typology to public usage data (68K prompts from WildChat and ThoughtTrace), we find that LLM-as-oracle use has increased over time (2023-2026) and is more prevalent among younger users. We further build a privacy-preserving data donation tool to analyze individuals' longitudinal usage data (140K prompts from 52 participants), identifying similar trends. People are often unaware of their own LLM-as-oracle use, and express dissatisfaction with this behavior after seeing our tool's analysis. Finally, we identify two drivers of LLM-as-oracle use: people's perceptions of AI and the behavior of AI models themselves, which motivate possible interventions to support users' self-deliberation.