Mg-doped indium oxide (In2O3) thin films were grown by plasma-assisted molecular beam epitaxy with Mg-concentrations ranging from 1017 to 6×1020 cm-3. In this concentration range Mg was incorporated into In2O3 without discernable impediment nor formation of secondary phases. Despite the role of Mg as acceptor, the films were n-type conductive in the as-grown state or after annealing in vacuum. For Mg-concentrations well in excess of the unintentional donor concentration annealing in oxygen resulted in semi-insulating films without detectable p-type conductivity. These results strongly suggest oxygen vacancies to act as shallow donors in In2O3 that can overcompensate the Mg acceptors.