Cuprous oxide (Cu2O) is a promising material for large scale photovoltaic applications. The efficiencies of thin film structures are, however, currently lower than those for structures based on Cu2O sheets, possibly due to their poorer transport properties. This study shows that post-deposition rapid thermal annealing (RTA) of Cu2O films is an effective approach for improving carrier transport in films prepared by reactive magnetron sputtering. The as-deposited Cu2O films were poly-crystalline, p-type, with weak near band edge (NBE) emission in photoluminescence spectra, a grain size of ~100 nm and a hole mobility of 2-18 cm2 V-1 s-1. Subsequent RTA (3 min) at a pressure of 50 Pa and temperatures of 600-1000 °C enhanced the NBE by 2-3 orders of magnitude, evidencing improved crystalline quality and reduction of non-radiative carrier recombination. Both grain size and hole mobility were increased considerably upon RTA, reaching values above 1 µm and up to 58 cm2 V-1 s-1, respectively, for films annealed at 900-1000 °C. These films also exhibited a resistivity of ~50-200 Ω cm, a hole concentration of ~1015 cm-3 at room temperature, and a transmittance above 80%.