We present the preparation and measurement of the radioactive isotope \(^{37}\textrm{Ar}\) , which was produced using thermal neutrons from a reactor, as a calibration source for liquid xenon time projection chambers. \(^{37}\textrm{Ar}\) is a low-energy calibration source with a half-life of 35.01 days, making it suitable for calibration in the low-energy region of liquid xenon dark-matter experiments. Radioactive isotope \(^{37}\textrm{Ar}\) was produced by irradiating \(^{36}\textrm{Ar}\) with thermal neutrons. It was subsequently measured in a gaseous xenon time projection chamber (GXe TPC) to validate its radioactivity. Our results demonstrate that \(^{37}\textrm{Ar}\) is an effective and viable calibration source that offers precise calibration capabilities in the low-energy domain of xenon-based detectors.