Catalyzes the 2'-O-methylation of the ribose of cytidine 1402 (C1402) in 16S rRNA. cytidine(1402) in 16S rRNA + S-adenosyl-L-methionine = 2'-O-methylcytidine(1402) in 16S rRNA + H(+) + S-adenosyl-L-homocysteine Belongs to the methyltransferase superfamily. RsmI family.