Cerebral X-ray digital subtraction angiography (DSA) is the standard imaging technique for visualizing blood flow and guiding endovascular treatments. The quality of DSA is often negatively impacted by body motion during acquisition, leading to decreased diagnostic value. Time-consuming iterative methods address motion correction based on non-rigid registration, and employ sparse key points and non-rigidity penalties to limit vessel distortion. Recent methods alleviate subtraction artifacts by predicting the subtracted frame from the corresponding unsubtracted frame, but do not explicitly compensate for motion-induced misalignment between frames. This hinders the serial evaluation of blood flow, and often causes undesired vasculature and contrast flow alterations, leading to impeded usability in clinical practice. To address these limitations, we present AngioMoCo, a learning-based framework that generates motion-compensated DSA sequences from X-ray angiography. AngioMoCo integrates contrast extraction and motion correction, enabling differentiation between patient motion and intensity changes caused by contrast flow. This strategy improves registration quality while being substantially faster than iterative elastix-based methods. We demonstrate AngioMoCo on a large national multi-center dataset (MR CLEAN Registry) of clinically acquired angiographic images through comprehensive qualitative and quantitative analyses. AngioMoCo produces high-quality motion-compensated DSA, removing motion artifacts while preserving contrast flow. Code is publicly available at https://github.com/RuishengSu/AngioMoCo.