A pn-heterojunction is fabricated by depositing an n-type β-Ga2O3 film by pulsed laser deposition (PLD) on c-cut Al2O3. P-type cuprous oxide films, Cu2O, are then deposited by PLD, as well as by radio frequency (RF) magnetron sputtering. It is concluded that hole injection is prohibited by a 3.26 eV valence band barrier, as measured by X-ray photo-electron spectroscopy (XPS) and ultraviolet photoelectron spectroscopy (UPS). Heterojunction diode structures are prepared on the front side and electrical measurements demonstrate a rectification ration of 8 orders of magnitude and an ideality factor close to 2, indicating interface recombination-controlled forward current. The junction is also optically active and shows a very fast photo-response to 275 nm UV light.