Drought stress is a key limiting factor for cotton (Gossypium spp.) growth, production, development, and production worldwide. Some wild diploid cotton species are remarkably tolerant of water deficit and constitute an important reservoir for understanding the molecular mechanisms of Gossypium spp. drought tolerance and improving cultivated upland cotton. Here, we utilized RNA-Seq technology to characterize the leaf transcriptomes of a wild African diploid cotton species, Gossypium anomalum, under drought stress. A total of 12,322 differentially expressed genes (DEGs) were identified after mapping valid clean reads to the reference genome of G. anomalum, of which 1243 were commonly differentially expressed at all stages of drought stress. These genes were significantly enriched for molecular functions Gene Ontology terms related to cytoskeleton, hydrolase activity, cellular redox, and binding. Additionally, a substantial proportion of enriched biological process terms concerned cell or subcellular processes, while most in the cellular components category concerned membrane function and photosynthesis. An enrichment analysis against the Kyoto Encyclopedia of Genes and Genomes showed the top significantly enriched pathways to be photosynthesis-antenna proteins, amino sugar and nucleotide sugar metabolism, starch and sucrose metabolism, MAPK signaling pathway, glutathione metabolism, and plant hormone signal transduction. The DEGs also exhibited interestingly significant enrichments for drought stress-induced tandemly repeated genes involved in iron ion binding, oxidoreductase activity, heme binding, and other biological processes. A large number of genes encoding transcription factors, such as MYB, bHLH, ERF, NAC, WRKY, and bZIP, were identified as playing key roles in acclimatizing to drought stress. These results will provide deeper insights into the molecular mechanisms of drought stress adaptation in Gossypium spp.