The D-genome progenitor of wheat (Triticum aestivum), Aegilops tauschii, possesses numerous genes for resistance to abiotic stresses, including drought. Therefore, information on the genetic architecture of A. tauschii can aid the development of drought-resistant wheat varieties. Here, we evaluated 13 traits in 373 A. tauschii accessions grown under normal and polyethylene glycol-simulated drought stress conditions and performed a genome-wide association study using 7,185 single nucleotide polymorphism (SNP) markers. We identified 208 and 28 SNPs associated with all traits using the general linear model and mixed linear model, respectively, while both models detected 25 significant SNPs with genome-wide distribution. Public database searches revealed several candidate/flanking genes related to drought resistance that were grouped into three categories according to the type of encoded protein (enzyme, storage protein, and drought-induced protein). This study provided essential information for SNPs and genes related to drought resistance in A. tauschii and wheat, and represents a foundation for breeding drought-resistant wheat cultivars using marker-assisted selection.