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The presence of small ions influences the growth dynamics of a size distribution of aerosols. Specifically, the often neglected mass of small ions influences the aerosol growth rate, which may be important for terrestrial cloud formation. To this end, we develop the Ion and Charged Aerosol Growth Enhancement (ION‐CAGE) code, a numerical model to calculate the growth of a species of aerosols in the presence of charge, which explicitly includes terms for ion condensation. It is shown that a positive contribution to aerosol growth rate is obtained by increasing the ion‐pair concentration through this ion condensation effect, consistent with recent experimental findings. The ion condensation effect is then compared to aerosol growth from charged aerosol coagulation, which is seen to be independent of ion‐pair concentration. Growth rate enhancements by ion condensation are largest for aerosol sizes less than ∼25 nm and increases proportional to the ion concentration. The effect of ion condensation is expected to be most important over pristine marine areas. The model source code is made available through a public repository. Plain Language Summary: It is unresolved whether there is a link between atmospheric ionization from galactic cosmic rays and terrestrial cloud formation. Support for the link is in part based on satellite observations and is further substantiated by recent laboratory experiments, which have detailed a microphysical aerosol mechanism that may give rise to this link. To test whether the mechanism can be the cause of the observed cosmic ray‐cloud link, numerical experiments are needed. In this article, we have developed an open‐source numerical model that allows for initial numerical experiments of this connection. Using the model, we show that atmospheric ions accelerate the growth of cloud precursor aerosols, which is consistent with the laboratory observations and supports the reality of the cosmic ray‐cloud link. Key Points: A numerical aerosol growth model is developed to consider growth of charged and neutral aerosolsThe model includes terms attributed to the condensation of small ion clusters onto aerosolsModeled growth rates are enhanced by ion condensation in agreement with recent experiments [ABSTRACT FROM AUTHOR]