Anisotropic multi-slice Cardiac Magnetic Resonance (CMR) Images are conventionally acquired in patient-specific short-axis (SAX) orientation. In specific cardiovascular diseases that affect right ventricular (RV) morphology, acquisitions in standard axial (AX) orientation are preferred by some investigators, due to potential superiority in RV volume measurement for treatment planning. Unfortunately, due to the rare occurrence of these diseases, data in this domain is scarce. Recent research in deep learning-based methods mainly focused on SAX CMR images and they had proven to be very successful. In this work, we show that there is a considerable domain shift between AX and SAX images, and therefore, direct application of existing models yield sub-optimal results on AX samples. We propose a novel unsupervised domain adaptation approach, which uses task-related probabilities in an attention mechanism. Beyond that, cycle consistency is imposed on the learned patient-individual 3D rigid transformation to improve stability when automatically re-sampling the AX images to SAX orientations. The network was trained on 122 registered 3D AX-SAX CMR volume pairs from a multi-centric patient cohort. A mean 3D Dice of 0.86 ± 0.06 for the left ventricle, 0.65 ± 0.08 for the myocardium, and 0.77 ± 0.10 for the right ventricle could be achieved. This is an improvement of 25% in Dice for RV in comparison to direct application on axial slices. To conclude, our pre-trained task module has neither seen CMR images nor labels from the target domain, but is able to segment them after the domain gap is reduced. Code: https://github.com/Cardio-AI/3d-mri-domain-adaptation.