Hello evablow, Welcome to the Sage ACT! Community. Unfortunately, there is not a way to sync contacts into the database via the web client. This would have to be done on the server that is hosting the actual database. You can only sync with ACT! if it is actually installed on your local machine.
Note: Effective 6/1/13, Sage no longers provides support for the Act! software. This is now provided by Swiftpage.