Aleatoric uncertainty negatively impacts registration and segmentation results for medical image analysis. In this paper, we propose an uncertainty-guided framework for the joint semi-supervised segmentation and registration of cardiac images, aiming to take advantage of both tasks for each other. We propose a semi-supervised segmentation framework by predicting statistical shape models of the heart and generating uncertainty maps to guide anchor selection in pixel-level contrastive learning. Besides, we develop a registration network to predict the deformation vector field (DVF) and registration uncertainty, where the registration uncertainty ensures the registration model focuses on regions with high confidence. By employing estimated DVFs, additional constraints between segmentation results are embedded as losses to further improve segmentation and registration accuracy at the same time. The experimental results show that our proposed framework outperforms the state-of-the-art registration and segmentation networks.