Catalysis of the reaction: adenosine2503 in 23S rRNA + 2 reduced - + 2 S-adenosyl-L-methionine = 2-methyladenosine2503 in 23S rRNA + 5'-deoxyadenosine + L-methionine + 2 oxidized - + S-adenosyl-L-homocysteine.
rRNA (adenine-C2-)-methyltransferase activity