Screening Papanicolaou test samples effectively reduces cervical cancer-related mortality, but the lack of trained cytopathologists prevents its widespread adoption in low-resource settings. Developing AI algorithms, e.g., deep learning to analyze the digitized cytology images suited to resource-constrained countries is appealing. Albeit successful, it comes at the price of collecting large annotated training datasets, which is both costly and time-consuming. Our study shows that the large number of unlabeled images that can be sampled from digitized cytology slides make for a ripe ground where self-supervised learning methods can thrive and even outperform off-the-shelf deep learning models on various downstream tasks. Along the same line, we report improved performance and data efficiency using modern augmentation strategies.