Sickle Cell Disease (SCD) is one of the most common genetic diseases in the world. Splenomegaly (abnormal enlargement of the spleen) is frequent among children with SCD. If left untreated, splenomegaly can be life-threatening. The current workflow to measure spleen size includes palpation, possibly followed by manual length measurement in 2D ultrasound imaging. However, this manual measurement is dependent on operator expertise and is subject to intra- and inter-observer variability. We investigate the use of deep learning to perform automatic estimation of spleen length from ultrasound images. We investigate two types of approach, one segmentation-based and one based on direct length estimation, and compare the results against measurements made by human experts. Our best model (segmentation-based) achieved a percentage length error of 7.42%, which is approaching the level of inter-observer variability (5.47%-6.34%). To the best of our knowledge, this is the first attempt to measure spleen size in a fully automated way from ultrasound images.