Radiotherapists require accurate registration of MR/CT images to effectively use information from both modalities. In a typical registration pipeline, rigid or affine transformations are applied to roughly align the fixed and moving images before proceeding with the deformation step. While recent learning-based methods have shown promising results in the rigid/affine step, these methods often require images with similar field-of-view (FOV) for successful alignment. As a result, aligning images with different FOVs remains a challenging task. Self-supervised landmark detection methods like self-supervised Anatomical eMbedding (SAM) have emerged as a useful tool for mapping and cropping images to similar FOVs. However, these methods are currently limited to intra-modality use only. To address this limitation and enable cross-modality matching, we propose a new approach called Cross-SAM. Our approach utilizes a novel iterative process that alternates between embedding learning and CT-MRI registration. We start by applying aggressive contrast augmentation on both CT and MRI images to train a SAM model. We then use this SAM to identify corresponding regions on paired images using robust grid-points matching, followed by a point-set based affine/rigid registration, and a deformable fine-tuning step to produce registered paired images. We use these registered pairs to enhance the matching ability of SAM, which is then processed iteratively. We use the final model for cross-modality matching tasks. We evaluated our approach on two CT-MRI affine registration datasets and found that Cross-SAM achieved robust affine registration on both datasets, significantly outperforming other methods and achieving state-of-the-art performance.