Anomaly detection is the process of identifying abnormal instances or events in datasets that deviate from the norm in a si- gnificant way. In this study, we propose a signature-based machine learning algorithm to detect rare or unexpected elements in a time series dataset. We present applications of signature or random signature as feature extractors for anomaly detection algorithms; in addition, we provide an easy representation-theoretic rationale for the construction of random signatures. Our first application is based on synthetic data and aims to distinguish between true and false stock price trajectories, which are indistinguishable by visual inspection. We also show a real-world application using transaction data from the crypto-currency market. In this case, we are able to identify organized pump-and-dump attempts on social networks with F1 scores of up to 88% using our unsupervised learning algorithm, achieving results close to the state-of-the-art in the field based on supervised learning.