One way of reducing the examination time in magnetic resonance imaging (MRI) is to reduce the amount of raw data acquired, by performing so-called undersampling. Conventionally, MRI data is acquired line-by-line on a Cartesian grid. In the field of Cardiovascular Magnetic Resonance (CMR), however, radial k-space sampling is seen as a promising emerging technique for rapid image acquisitions, mainly due to its robustness against motion disturbances occurring from the beating heart. Whereas Cartesian undersampling will result in image aliasing, radial undersampling will introduce streak artifacts. The objective of this work was to train the deep learning architecture, CycleGAN, to reduce streak artifacts in radially undersampled CMR images, and to evaluate the model performance. A benefit of using CycleGAN over other deep learning techniques for this application is that it can be trained on unpaired data. In this work, CycleGAN network was trained on 3060 radial and 2775 Cartesian unpaired CMR images acquired in human subjects to learn a mapping between the two image domains. The model was evaluated in comparison to images reconstructed using another emerging technique called GRASP. Whereas more investigation is warranted, the results are promising, suggesting that CycleGAN could be a viable method for effective streak-reduction in clinical applications.