This paper reports the irradiation of the production version of the readout chip for the CMS HL-LHC pixel detector, CROC~v2, to 1.6~Grad using $\gamma$s from a $^{60}$Co source at Sandia National Laboratory. The CROC~v2 was kept powered, configured, and maintained as close as possible to its nominal operating temperature of -20~$^{\rm o}$C during irradiation. Internal chip voltages, pixel response, and diagnostic ring oscillators were continuously monitored, and thresholds were optimized frequently. The CROC~v2 performed according to specifications at 1.6~Grad. Where available, these results will be compared with those for this and earlier iterations of the RD53 readout chip irradiated to a few Grad with lower-energy X-ray sources.