Automatic identification of screw types is important for industrial automation, robotics, and inventory management. However, publicly available datasets for screw classification are scarce, particularly for controlled single-object scenarios commonly encountered in automated sorting systems. In this work, we introduce $\textbf{SortScrews}$, a dataset for casewise visual classification of screws. The dataset contains 560 RGB images at $512\times512$ resolution covering six screw types and a background class. Images are captured using a standardized acquisition setup and include mild variations in lighting and camera perspective across four capture settings. To facilitate reproducible research and dataset expansion, we also provide a reusable data collection script that allows users to easily construct similar datasets for custom hardware components using inexpensive camera setups. We establish baseline results using transfer learning with EfficientNet-B0 and ResNet-18 classifiers pretrained on ImageNet. In addition, we conduct a well-explored failure analysis. Despite the limited dataset size, these lightweight models achieve strong classification accuracy, demonstrating that controlled acquisition conditions enable effective learning even with relatively small datasets. The dataset, collection pipeline, and baseline training code are publicly available at https://github.com/ATATC/SortScrews.