Catalyzes the specific phosphorylation of arginine residues in proteins. ATP + L-arginyl-[protein] = ADP + H(+) + N(omega)-phospho-L-arginyl-[protein] Appears to be allosterically activated by the binding of pArg-containing polypeptides to the pArg-binding pocket localized in the C-terminal domain of McsB. Belongs to the ATP:guanido phosphotransferase family.