We present ab initio calculations of the collisional broadening of the R(0) pure rotational line in CO (at 115 GHz) perturbed by O2. Our calculations are done in a fully quantum way by solving close-coupling quantum-scattering equations without any approximations. We also report a new, highly accurate CO-O2 potential energy surface on which we did the quantum-scattering calculations. The calculated collisional broadening agrees with the available experimental data in a wide temperature range. The calculated collisional shift is negligible compared to the broadening, which is also consistent with the experimental data. We combine this result with our previous calculations for the same line in CO perturbed by N2 [Jóźwiak et al., J. Chem. Phys. 154, 054314 (2021)]; the obtained air-perturbed broadening of the R(0) pure rotational line in CO and its temperature dependence perfectly agree with the HITRAN database. This result constitutes an important step toward developing a methodology for providing accurate ab initio reference data on spectroscopic collisional line-shape parameters for molecular systems relevant to the Earth's atmosphere and for populating spectroscopic line-by-line databases.