You don't. ODBC is a connection method not a database type. You create the database as normal, ensure you have the ODBC drivers installed and then create the connection. See http://dev.mysql.com/doc/refman/5.5/en/connector-odbc.html
Yes you are absolutely right we can't create ODBC database because Open Data Base Connectivity, a standard database access method developed by the SQL Access group in 1992. The goal of ODBC is to make it possible to access any data from any application, regardless of which database management system (DBMS) is handling the data.
Since your MySQL tables are hosted, you'll probably be limited by the capabilities of what's on the hosting instance. If you have total control of the server, you can install an ODBC connector, but I'm assuming you don't.