The study of human evolution has been revolutionized by inferences from ancient DNA analyses. Key to these is the reliable estimation of the age of ancient specimens. The current best practice is radiocarbon dating, which relies on characterizing the decay of radioactive carbon isotope (14C), and is applicable for dating up to 50,000-year-old samples. Here, we introduce a new genetic method that uses recombination clock for dating. The key idea is that an ancient genome has evolved less than the genomes of extant individuals. Thus, given a molecular clock provided by the steady accumulation of recombination events, one can infer the age of the ancient genome based on the number of missing years of evolution. To implement this idea, we take advantage of the shared history of Neanderthal gene flow into non-Africans that occurred around 50,000 years ago. Using the Neanderthal ancestry decay patterns, we estimate the Neanderthal admixture time for both ancient and extant samples. The difference in these admixture dates then provides an estimate of the age of the ancient genome. We show that our method provides reliable results in simulations. We apply our method to date five ancient Eurasian genomes with radiocarbon dates ranging between 12,000 to 45,000 years and recover consistent age estimates. Our method provides a complementary approach for dating ancient human samples and is applicable to ancient non-African genomes with Neanderthal ancestry. Extensions of this methodology that use older shared events may be able to date ancient genomes that fall beyond the radiocarbon frontier.