Anxiety is a widespread and serious mental health issue that has been exacerbated by the COVID-19 pandemic and other stressors. In this study, we explore how online behavior data from Google and YouTube can be used to infer anxiety levels in individuals. We collected and processed digital traces from nearly 100 participants over eight weeks and applied various machine learning techniques to extract features and build predictive models. We found that combining data from multiple media modalities can yield highly accurate predictive models for anxiety as self-reported by a clinical GAD-7 scale (AUC > 0.86). We also found that the semantic categories of online engagement can affect the predictive performance of the models. This study contributes to the field of computational social science and digital mental health and demonstrates the potential of using online behavior data to monitor psychological well-being and design interventions for anxiety.