In this brief, the total ionizing dose (TID) effects of γ rays generated from a 60Co source on the TaOx-based resistive switching memory (resistive random-access memory, RRAM) is investigated. The low-resistance state (LRS) of the RRAM is immune to TID effects, whereas the sensitivity of the high-resistance state (HRS) of RRAM to TID effects depends on the dimensions of the device, including the thickness of the oxide film and the area of the device. The HRS of the device with large area and thick oxide layer is vulnerable to TID effects and has a high probability to change into the LRS. Further investigation found that the lower the high resistance, the higher the failure rate of the RRAM device under TID impact, which indicates that the multilevel cell of RRAM should be carefully designed for space system applications considering the radiation effects. The failure of the HRS under TID is explained by defect generation in the oxide film.