We have experimentally determined the production rate of 39 Ar and 37 Ar due to cosmic ray neutron interactions in argon at sea level. Understanding these production rates is important for argon-based dark matter experiments that plan to utilize argon extracted from deep underground because it is imperative to know what the ingrowth of 39 Ar will be during the production, transport, and storage of the underground argon. These measurements also allow for the prediction of 39 Ar and 37 Ar concentrations in the atmosphere which can be used to determine the presence of other sources of these isotopes. Through controlled irradiation with a neutron beam that mimics the cosmic ray neutron spectrum, followed by direct counting of 39 Ar and 37 Ar decays with sensitive ultra-low background proportional counters, we determined that the production rate from cosmic ray neutrons at sea-level is expected to be (759 ± 128) atoms/(kg Ar day) for 39 Ar, and (51.0 ± 7.4) atoms/(kg Ar day) for 37 Ar. We also performed a survey of the alternate production mechanisms based on the state-of-knowledge of the associated cross-sections to obtain a total sea-level cosmic ray production rate of (1048 ± 133) atoms/(kg Ar day) for 39 Ar, (56.7 ± 7.5) atoms/(kg Ar day) for 37 Ar in underground argon, and (92 ± 13) atoms/(kg Ar day) for 37 Ar in atmospheric argon.