In the deeper part of polar ice sheets, air hydrates are the primary air inclusions. They trap most of the ancient air molecules used for paleoclimatic reconstructions in their crystal structure. This dataset presents the first Electron Backscatter Diffraction (EBSD) measurements on air hydrates included in the EDML ice core. The sample was originally located at 2045.3 m depth. EBSD is a technique to characterize the microstructure of materials, which includes the precise determination of crystallographic orientations of measured materials. The measurements were taken by Florian Painer, Martyn Drury and Maartje Hamers at the University of Utrecht. The aim was to investigate the crystallographic nature and measure the crystallographic orientation of air hydrates included in polar ice. We thank Eric Hellebrand and Erik Betz-Güttner for their support in operating the Cryo-SEM. Access to the Cryo-SEM at MINT-UU (Utrecht University) was provided by EPOS-NL Facility Access, supported by the Dutch Research Council (NWO).