To evaluate the role of radio activity in galaxy evolution, we designed a large archival CO survey of radio galaxies (RGs) to determine their molecular gas masses at different epochs. We used a sample of 120 RGs representative of the NVSS 1.4GHz survey, when flux limited at 0.4Jy. Of those, 66 galaxies belonged to the ALMA Radio-source Catalogue (ARC) of calibrators and had spectral window tunings around CO (1-0), (2-1), (3-2), or (4-3). We reduced their ALMA data, determined their H2 mass contents, and combined the results with similar results for the remaining 54 galaxies from the literature. We found that, while at all epochs the majority of RGs have undetectable reservoirs, there is a rapid increase in the H2 mass content of the CO-detected RGs with z. At 1