In this work, we demonstrate the fabrication of CuxO/Ga2O3 heterojunction through the spontaneous oxidation of Cu film into CuxO layer during electron beam evaporation. The heterojunction device presents a ultraviolet (UV)/visible rejection ratio ( ${R}_{{265}}/{R}_{{430}}$ ) at zero bias of 435, enabling the self-powered deep-UV (DUV) photodetection. Upon 265-nm illumination (light intensity: $21.7 \mu \text{W}\cdot $ cm $^{-{2}}$ ), the responsivity ( $R$ ) and specific detectivity ( $\text{D}^{\ast} $ ) reach 0.97 mA $\cdot \text{W}^{-{1}}$ and $6.28\times 10^{{10}}$ Jones, respectively. A fast response speed of 5.34/3.64 ms ( $\tau _{r}/\tau _{f}$ ) has also been observed, which may ascribe to the fully depleted thin CuxO layer and suggest the ability to detect rapidly switched optical signal. This work sheds light on the facile fabrication of $\beta $ -Ga2O3-based self-powered DUV photodetectors.