Side-scan sonar (SSS) is a lightweight acoustic sensor that is frequently deployed on autonomous underwater vehicles (AUVs) to provide high-resolution seafloor images. However, using side-scan images to perform simultaneous localization and mapping (SLAM) remains a challenge when there is a lack of 3D bathymetric information and discriminant features in the side-scan images. To tackle this, we propose a feature-based SLAM framework using side-scan sonar, which is able to automatically detect and robustly match keypoints between paired side-scan images. We then use the detected correspondences as constraints to optimize the AUV pose trajectory. The proposed method is evaluated on real data collected by a Hugin AUV, using as a ground truth reference both manually-annotated keypoints and a 3D bathymetry mesh from multibeam echosounder (MBES). Experimental results demonstrate that our approach is able to reduce drifts from the dead-reckoning system. The framework is made publicly available for the benefit of the community.