You have options.

When using Standard Edition or higher, when a Merge subscription is created, an associated Merge Agent job is created. You start the job to synchronize the subscription.

You can invoke the Merge Agent executable, replmerg.exe, and pass the appropriate parameters to synchronize the subscription.

RMO via C# or VB.NET is an option in 2012 or earlier but it has been deprecated and I believe it has been removed in 2014.