Targeted phishing emails are on the rise and facilitate the theft of billions of dollars from organizations a year. While malicious signals from attached files or malicious URLs in emails can be detected by conventional malware signatures or machine learning technologies, it is challenging to identify hand-crafted social engineering emails which don't contain any malicious code and don't share word choices with known attacks. To tackle this problem, we fine-tune a pre-trained BERT model by replacing the half of Transformer blocks with simple adapters to efficiently learn sophisticated representations of the syntax and semantics of the natural language. Our Context-Aware network also learns the context representations between email's content and context features from email headers. Our CatBERT(Context-Aware Tiny Bert) achieves a 87% detection rate as compared to DistilBERT, LSTM, and logistic regression baselines which achieve 83%, 79%, and 54% detection rates at false positive rates of 1%, respectively. Our model is also faster than competing transformer approaches and is resilient to adversarial attacks which deliberately replace keywords with typos or synonyms.