The performance and diagnostic utility of magnetic resonance imaging (MRI) in pregnancy is fundamentally constrained by fetal motion. Motion of the fetus, which is unpredictable and rapid on the scale of conventional imaging times, limits the set of viable acquisition techniques to single-shot imaging with severe compromises in signal-to-noise ratio and diagnostic contrast, and frequently results in unacceptable image quality. Surprisingly little is known about the characteristics of fetal motion during MRI and here we propose and demonstrate methods that exploit a growing repository of MRI observations of the gravid abdomen that are acquired at low spatial resolution but relatively high temporal resolution and over long durations (10-30 minutes). We estimate fetal pose per frame in MRI volumes of the pregnant abdomen via deep learning algorithms that detect key fetal landmarks. Evaluation of the proposed method shows that our framework achieves quantitatively an average error of 4.47 mm and 96.4% accuracy (with error less than 10 mm). Fetal pose estimation in MRI time series yields novel means of quantifying fetal movements in health and disease, and enables the learning of kinematic models that may enhance prospective mitigation of fetal motion artifacts during MRI acquisition.