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We report on the realization of Atom Trap Trace Analysis for ³⁹Ar and its first application to dating of groundwater samples. The presented system achieves an atmospheric ³⁹Ar count rate as high as 3.58 ± 0.10 atoms/h allowing for the determination of the ³⁹Ar concentration in less than a day. We demonstrate that the measured count rates are proportional to the ³⁹Ar concentration by intercomparison with Low-Level Counting results and by measurements on prepared argon samples with defined concentration. For a geophysical application, we degas three different groundwater samples and gas chromatographically extract the argon. The ³⁹Ar ages inferred from the count rates extend over the accessible dating range and are in agreement with the Low-Level Counting results as well as with complementary isotope data.