Augmented reality (AR) systems pose unique privacy risks due to their continuous capture of visual data. Existing AR privacy frameworks lack semantic understanding of visual content, limiting their effectiveness in detecting context-dependent privacy risks. We propose PrivAR, which leverages vision language models (VLMs) with chain-of-thought prompting for contextual privacy risk detection in AR environments. PrivAR uses visual scene cues to infer potential sensitive information types, such as identifying password notes in office environments through contextual reasoning. PrivAR detects and obfuscates textual content, preventing exposure of sensitive information while preserving contextual cues necessary for VLM inference. Additionally, we investigate contextually-informed warning interfaces to enhance user privacy awareness. Experiments on a real-world AR dataset show that PrivAR achieves superior accuracy (81.48%) and F1-score (84.62%) compared to baselines, while reducing privacy leakage rate to 17.58%. User studies evaluating contextually-informed warning interfaces provide insights into effective privacy-aware AR design.