The study of human evolution has been revolutionized by inferences from ancient DNA analyses. Key to these studies is the reliable estimation of the age of ancient specimens. High-resolution age estimates can often be obtained using radiocarbon dating, and, while precise and powerful, this method has some biases, making it of interest to directly use genetic data to infer a date for samples that have been sequenced. Here, we report a genetic method that uses the recombination clock. The idea is that an ancient genome has evolved less than the genomes of present-day individuals and thus has experienced fewer recombination events since the common ancestor. To implement this idea, we take advantage of the insight that all non-Africans have a common heritage of Neanderthal gene flow into their ancestors. Thus, we can estimate the date since Neanderthal admixture for present-day and ancient samples simultaneously and use the difference as a direct estimate of the ancient specimen's age. We apply our method to date five Upper Paleolithic Eurasian genomes with radiocarbon dates between 12,000 and 45,000 y ago and show an excellent correlation of the genetic and (14)C dates. By considering the slope of the correlation between the genetic dates, which are in units of generations, and the (14)C dates, which are in units of years, we infer that the mean generation interval in humans over this period has been 26-30 y. Extensions of this methodology that use older shared events may be applicable for dating beyond the radiocarbon frontier.