Catalysis of the reaction: S-adenosyl-L-methionine + (histone H3)-arginine (position 8) = S-adenosyl-L-homocysteine + (histone H3-N-methyl-arginine (position 8). This reaction is the addition of a methyl group to the arginine residue at position 8 of histone H3.
histone H3R8 arginine methyltransferase activity