Although controversial, many observations have suggested that low-level cloud cover correlates with the cosmic ray flux. Because galactic cosmic rays have likely decreased in intensity over the last century, this hypothesis, if true, could partly explain 20th century warming, thereby upsetting the consensus view that greenhouse-gas forcing has caused most of the warming. The “ion-aerosol clear-air” hypothesis suggests that increased cosmic rays cause increases in new-particle formation, cloud condensation nuclei concentrations (CCN), and cloud cover. In this paper, we present the first calculations of the magnitude of the ion-aerosol clear-air mechanism using a general circulation model with online aerosol microphysics. In our simulations, changes in CCN from changes in cosmic rays during a solar cycle are two orders of magnitude too small to account for the observed changes in cloud properties; consequently, we conclude that the hypothesized effect is too small to play a significant role in current climate change.