Georegistration of digital elevation maps is a vital step in fusing sensor data. In this paper, we present an entropic registration method using Morse singularities. The core idea behind our proposed approach is to encode an elevation map into a set of Morse singular points. Then an information-theoretic dissimilarity measure between the Morse features of the target and the reference maps is maximized to bring the elevation data into alignment. We also show that maximizing this divergence measure leads to minimizing the total length of the joint minimal spanning tree of both elevation data maps. Illustrating experimental results are presented to show the robustness and the georegistration accuracy of the proposed approach.