Cine cardiac magnetic resonance imaging (MRI) is widely used for diagnosis of cardiac diseases thanks to its ability to present cardiovascular features in excellent contrast. As compared to computed tomography (CT), MRI, however, requires a long scan time, which inevitably induces motion artifacts and causes patients discomfort. Thus, there has been a strong clinical motivation to develop techniques to reduce both the scan time and motion artifacts. Given its successful applications in other medical imaging tasks such as MRI super-resolution and CT metal artifact reduction, deep learning is a promising approach for cardiac MRI motion artifact reduction. In this paper, we propose a recurrent neural network to simultaneously extract both spatial and temporal features from under-sampled, motion-blurred cine cardiac images for improved image quality. The experimental results demonstrate substantially improved image quality on two clinical test datasets. Also, our method enables data-driven frame interpolation at an enhanced temporal resolution. Compared with existing methods, our deep learning approach gives a superior performance in terms of structural similarity (SSIM) and peak signal-to-noise ratio (PSNR).