Suboptimal generalization of machine learning models on unseen data is a key challenge which hampers the clinical applicability of such models to medical imaging. Although various methods such as domain adaptation and domain generalization have evolved to combat this challenge, learning robust and generalizable representations is core to medical image understanding, and continues to be a problem. Here, we propose STRAP (Style TRansfer Augmentation for histoPathology), a form of data augmentation based on random style transfer from artistic paintings, for learning domain-agnostic visual representations in computational pathology. Style transfer replaces the low-level texture content of images with the uninformative style of randomly selected artistic paintings, while preserving high-level semantic content. This improves robustness to domain shift and can be used as a simple yet powerful tool for learning domain-agnostic representations. We demonstrate that STRAP leads to state-of-the-art performance, particularly in the presence of domain shifts, on a particular classification task of predicting microsatellite status in colorectal cancer using digitized histopathology images.