Rare-earth-barium-copper-oxide (REBCO) coated conductor tapes within next-generation tokamak pilot and power plant magnets will be exposed to broad-spectrum gamma-ray and neutron irradiation concurrently. It has been known since the 1980s that cumulative neutron fluence affects the superconducting properties of REBCO, but the effects of gamma rays are less certain, as are the effects of radiation (of any kind) during current flow. However, the use of superconductors as photon detectors suggests that energetic photons interact directly with the superconducting state, locally destroying superconductivity. Hence, as well as the effect of the overall radiation dose (fluence), the effect of radiation dose rate (flux) on the superconductor’s properties must be quantified to understand how REBCO magnets will perform during fusion magnet operation. In-situ measurements of the self-field critical current at 77 K, of several REBCO coated conductor tapes were performed during Co-60 gamma ray exposure at a dose rate of 86 Gy min⁻¹ . Samples were fully submerged in liquid nitrogen throughout the measurements. No change in the critical current of any sample during or after irradiation was observed within standard error. These are the first reported in-situ measurements of critical current during fusion-relevant gamma irradiation. Two samples were irradiated to a further dose of 208 kGy at room temperature and a second round of in-situ measurements was performed. No change in the critical current of these samples was observed within standard error. This corroborates recent studies, but is in conflict with older literature.