In this study, a novel computational method was developed to investigate the transport characteristics of ions in gas-filled radiation detectors, which are closely linked to the behavior of ions in gaseous detectors. Parameters such as polarizability, mean free path, collision frequency, and mean free time, which directly impact ion mobility, were physically manipulated using the Monte Carlo technique, and the results were validated against fundamental physical principles. As an initial scenario, computations were performed on the mobility of Ar+ ions in an argon environment as a carrier gas. The distribution of the radial velocity components of the ion following an ion-gas collision was represented as a two-dimensional histogram with a disc-shaped pattern, and this result was elucidated utilizing the Maxwell-Boltzmann distribution. The findings regarding the mean free time and mean free path of an Ar+ ion in an argon carrier gas align with the results derived from Skullerud's methodologies. These findings hold promise for Garfield++ simulations, enabling the computation of ion mobility and even cluster ions in the mixture, thereby considering their impact on the detector's gain parameters. The results of this investigation offer novel insights into the behavior of ions within detector settings, significantly enhancing our comprehension of the mobility of ions and its effects on radiation detection efficiency.