How do I guarantee using Microsoft ODBC Driver 13 for SQL Server in a linked server?
It's not possible to use just ODBC. Linked servers use Distributed Queries which is dependent on the OLEDB interface. This is not an optional or interchangeable API. Below that API can be any OLEDB, ODBC or even JDBC provider so long as its implementation supports the OLEDB interface. For example, there is an OLEDB provider for ODBC which is one of the most common ways to run DQ against non-SQL Server data sources. SQL Server natively supports OLEDB so there's no need for the extra layer. Most/all of this information can be found in Books Online or MSDN.

Why do you need to use only ODBC? If want it for Always Encrypted, suggest you log a feature request via https://connect.microsoft.com/SQLServer/feedback/. I don't know if the scenario is even supported where you run AE through DQ. The "calling SQL Server" essentially becomes the client to the "target SQL Server" but you don't fully control the client since DQ isn't something you can modify. 

If it's for some other reason, share details here so folks help come up with alternate solutions.