Reliable values of the viscosity in thermal argon plasmas are most important for our understanding of the momentum transfer and for realistic modeling of various plasma applications. Despite numerous attempts to determine reliable viscosity values over the last three decades, discrepancies still exist among the data reported by different authors. In this paper, a critical analysis is undertaken of calculated and experimental data of the argon viscosity based on recent publications. Our recalculation of viscosities in thermal argon plasmas are performed by using Lennard-Jones, Morse, Aziz, and exponential repulsive potentials for Ar-Ar atom interactions in different temperature ranges from 300 to 20,000 K. The contributions of elastic collisions of e-Ar, e-Ar+, and Ar+-Av, as well as charge exchange of Ar+-Ar, to the viscosity became important with increasing temperature and degree of ionization in argon plasmas. Based on a critical analysis and recalculations, improved values of the argon viscosity are recommended, covering temperatures from 300 to 20,000 K. Polynomial expressions have been developed for calculating argon viscosities, which will be useful for numerical work and other applications of thermal argon plasmas at atmospheric pressure.