Catalyzes electroneutral exchange between arginine and ornithine to allow high-efficiency energy conversion in the arginine deiminase pathway. L-arginine(out) + L-ornithine(in) = L-arginine(in) + L-ornithine(out) Belongs to the amino acid-polyamine-organocation (APC) superfamily. Basic amino acid/polyamine antiporter (APA) (TC 2.A.3.2) family.