We report on the magnetic and structural properties of Cr-doped GaN prepared by ion implantation of epitaxial thin films. Based on a detailed analysis of the magnetometry data, we demonstrate that the magnetic interactions between Cr moments in GaN are antiferromagnetic (AFM). Increasing the Cr fractional concentration up to 0.35, we observe that strong nearest cation neighbor AFM coupling results in the reduction of the effective moment per Cr atom. The uncompensated Cr moments exhibit paramagnetic behavior and we discuss to what extent the effects of an anisotropic crystal field and AFM interactions can be inferred from the magnetization data. We discuss the observed changes in magnetic and structural properties induced by thermal annealing in terms of defect annealing and Cr aggregation.