In this study, Gd ion implantation and annealing were performed at ${900}^{\ensuremath{\circ}}\phantom{\rule{0.16em}{0ex}}\mathrm{C}$ for nominally undoped wurtzite GaN grown by metal-organic chemical vapor deposition. Spin-polarized positron annihilation measurements showed that vacancy clusters including at least 12 vacancies per cluster were the major positron-trapping centers and that the electrons in the vacancy clusters were spin-polarized. These observations could be explained by first-principles calculations. The previous speculation about the defect-assisted ferromagnetism of Gd-implanted GaN may be supported if vacancy clusters are considered.