We present an investigation of the (222)Rn concentration in argon with ultra-low background proportional counters. Argon purification tests by means of cryo-adsorption of radon on activated carbon were performed. For gaseous argon the purification process was found to be very efficient. Also in liquid phase the (222)Rn concentration could be reduced significantly, however, the efficiency is lower than in the gas phase. We also have analyzed the initial (222)Rn concentrations in commercial liquid argon. It was found to be significantly higher than in liquid nitrogen.