Anxiety disorder is one of the most prevalent mental health conditions globally, arising from complex interactions of biological and environmental factors and severely interfering with one's ability to lead normal life activities. Current methods for detecting anxiety heavily rely on in-person interviews, which can be expensive, time-consuming, and blocked by social stigmas. We propose an alternative method to identify individuals with anxiety and further estimate their levels of anxiety using personal online activity histories from YouTube and the Google Search engine. We ran a longitudinal study and collected multiple rounds of anonymized YouTube and Google Search logs from volunteering participants, along with their clinically validated ground-truth anxiety assessment scores. We then developed explainable features that capture both the temporal and contextual aspects of online behaviors. Using those, we were able to train models that can (i) identify individuals having anxiety disorder (ii) assess the level of anxiety by accurately predicting the gold standard Generalized Anxiety Disorder 7-item scores based on the ubiquitous individual-level online engagement data. Our proposed anxiety assessment framework can be deployed in clinical settings, empowering care providers to learn about anxiety disorders of patients non-invasively.