Zr-doped HfO2(HZO)-based germanium (Ge) p-channel ferroelectric FET (p-FeFET) memory devices with microwave annealing (MWA) followed by rapid thermal annealing (RTA) are employed as the platform to investigate the impact of <inline-formula> <tex-math notation="LaTeX">\gamma </tex-math></inline-formula>-ray radiation on the device performance. With a radiation dose of 1 Mrad, the memory window (MW) degrades from 2.5 V to 2.0 V accompanied by the significantly increased off-state current. The deleterious radiation effect is ascribed to the susceptible quality of the interface between the gate dielectric and source/drain region due to exacerbated charge trapping for the Ge substrate. These trapped charges also screen the polarization charges after applying a voltage pulse and lead to increased read-after-write latency. Nevertheless, compared with the irradiated HfO2-based FeFET memories in the literature, the Ge p-FeFETs in this work demonstrate competitive anti-radiation capability in terms of a large MW of 1.5 V even after <inline-formula> <tex-math notation="LaTeX">10^{{5}} </tex-math></inline-formula> cycles by bipolar stress (±4 V/<inline-formula> <tex-math notation="LaTeX">1~\mu \text{s} </tex-math></inline-formula>) and desirable retention up to 10 years under low voltage operation.