Catalysis of the reaction: S-adenosyl-L-methionine + vitexin 2''-O-beta-L-rhamnoside = S-adenosyl-L-homocysteine + 7-O-methylvitexin 2''-O-beta-L-rhamnoside.
S-adenosyl-L-methionine:vitexin-2\'\'-O-beta-L-rhamnoside 7-O-methyltransferase activity