Catalysis of the reaction: S-adenosyl-L-methionine + (histone H4)-arginine (position 3) = S-adenosyl-L-homocysteine + (histone H4)-N-methyl-arginine (position 3). This reaction is the addition of a methyl group to the arginine residue at position 3 of histone H4, producing histone H4R3me.
histone methylase activity (H4-R3 specific)