The 1-Mb and 4-Mb commercial toggle magnetoresistive random-access memories (MRAMs) with 0.13 µm and 0.18µm complementary metal-oxide-semiconductor (CMOS) process respectively and different magnetic tunneling junctions (MTJs) are irradiated with a Cobalt-60 gamma source. The electrical functions of devices during the irradiation and the room temperature annealing behavior are measured. Electrical failures are observed until the dose accumulates to 120-krad (Si) in 4-Mb MRAM while the 1-Mb MRAM keeps normal. Thus, the 0.13-µm process circuit exhibits better radiation tolerance than the 0.18-µm process circuit. However, a small quantity of read bit-errors randomly occurs only in 1-Mb MRAM during the irradiation while their electrical function is normal. It indicates that the store states of MTJ may be influenced by gamma radiation, although the electrical transport and magnetic properties are inherently immune to the radiation. We propose that the magnetic Compton scattering in the interaction of gamma ray with magnetic free layer may be the origin of the read bit-errors. Our results are useful for MRAM toward space application.