There is support with some caveats specifically around the always connect feature. "Apple iOS 7 no longer supports Always Connect domains. When running AnyConnect on Apple iOS 7 devices, any domains listed as Always Connect will be treated as Connect if Needed domains."
There is a list of devices supported and iOS compatibilities found here http://www.cisco.com/en/US/docs/security/vpn_client/anyconnect/anyconnect30/administration/guide/acmobiledevices.html
