Libraries are digitizing their collections of maps from all eras, generating increasingly large online collections of historical cartographic resources. Aligning such maps to a modern geographic coordinate system greatly increases their utility. This work presents a method for such automatic georeferencing, matching raster image content to GIS vector coordinate data. Given an approximate initial alignment that has already been projected from a spherical geographic coordinate system to a Cartesian map coordinate system, a probabilistic shape-matching scheme determines an optimized match between the GIS contours and ink in the binarized map image. Us- ing an evaluation set of 20 historical maps from states and regions of the U.S., the method reduces average alignment RMSE by 12%