Rational design of single-metal atom sites in carbon substrates by a flexible strategy is highly desired for the preparation of high-performance catalysts for metal-air batteries. In this study, biomass hydrogel reactors are utilized as structural templates to prepare carbon aerogels embedded with single iron atoms by controlled pyrolysis. The tortuous and interlaced hydrogel chains lead to the formation of abundant nanowrinkles in the porous carbon aerogels, and single iron atoms are dispersed and stabilized within the defective carbon skeletons. X-ray absorption spectroscopy measurements indicate that the iron centers are mostly involved in the coordination structure of FeN4, with a minor fraction (ca. 1/5) in the form of FeN3C. First-principles calculations show that the FeN x sites in the Stone-Wales configurations induced by the nanowrinkles of the hierarchically porous carbon aerogels show a much lower free energy than the normal counterparts. The resulting iron and nitrogen-codoped carbon aerogels exhibit excellent and reversible oxygen electrocatalytic activity, and can be used as bifunctional cathode catalysts in rechargeable Zn-air batteries, with a performance even better than that based on commercial Pt/C and RuO2 catalysts. Results from this study highlight the significance of structural distortions of the metal sites in carbon matrices in the design and engineering of highly active single-atom catalysts.