Time series observations of a single dithered field centred on the diffuse dwarf satellite galaxy Crater II were obtained with the Dark Energy Camera (DECam) at the 4m Blanco Telescope at Cerro Tololo Inter-American Observatory, Chile, uniformly covering up to two half-light radii. Analysis of the g and i time series results in the identification and characterization of 130 periodic variable stars, including 98 RR Lyrae stars, 7 anomalous Cepheids, and 1 SX Phoenicis star belonging to the Crater II population, and 24 foreground variables of different types. Using the large number of ab-type RR Lyrae stars present in the galaxy, we obtained a distance modulus to Crater II of (m - M)0 = 20.333 ± 0.004 (stat) ±0.07 (sys). The distribution of the RR Lyrae stars suggests an elliptical shape for Crater II, with an ellipticity of 0.24 and a position angle of 153°. From the RR Lyrae stars, we infer a small metallicity dispersion for the old population of Crater II of only 0.17 dex. There are hints that the most metal-poor stars in that narrow distribution have a wider distribution across the galaxy, while the slightly more metal-rich part of the population is more centrally concentrated. Given the features in the colour-magnitude diagram of Crater II, the anomalous Cepheids in this galaxy must have formed through a binary evolution channel of an old population.