Collision cross sections and transport coefficients are calculated for Ar+ and Ar2+ ions, in the ground and metastable states, colliding with gaseous Ar. These basic data are of great interest for a better understanding of physical and chemical properties of the plasma jet using argon as carrier gas. The needed collision cross sections were determined using a close coupling quantum method for the mono-atomic ion colliding with its parent gas. For the diatomic ion, a hybrid approach, mixing classical and quantum dynamics, and an “inverse” method, based on a simplified spherical potential, were used. The ion transport coefficients are calculated from the corresponding collision cross sections by using an optimized Monte Carlo code over a wide range of reduced electric field. Calculated transport coefficients are compared with available experimental data.