Icebergs release cold, fresh meltwater and terrigenous nutrients as they drift and melt, influencing the local ocean properties, encouraging sea ice formation and biological production. To locate and quantify the fresh water flux from Antarctic icebergs, changes in their area and thickness have to be monitored along their trajectories. While the locations of large icebergs are operationally tracked by manual inspection, delineation of their extent is not. Here, we propose a U-net approach to automatically map the extent of giant icebergs in Sentinel-1 imagery. This greatly improves the efficiency compared to manual delineations, reducing the time for each outline from several minutes to less than 0.01 s. We evaluate the performance of our U-net and two state-of-the-art segmentation algorithms (Otsu and k-means) on 191 images. For icebergs larger than those covered by the training data, we find that U-net tends to miss parts. Otherwise, U-net is more robust in scenes with complex backgrounds - ignoring sea ice, smaller regions of nearby coast or other icebergs - and outperforms the other two techniques by achieving an F1 score of 0.84 and an absolute median deviation in iceberg area of 4.1 %.