I think no one has replied because the question doesn't quite work. The US funded revolutions etc in the context of a bipolar world; that didn't really exist for Rome.

Rome did, of course, support some countries or tribes against others (Caesar assisted the Gauls against Ariovistus, for instance), but there wasn't the kind of ideological problem that existed between the US and the USSR. Even when Rome was fighting with the Parthians, I can't imagine an ideological dispute - it was just territory that mattered, as far as I know. If someone out there knows more I will appreciate being corrected.