Right-wing, at least in the context of American politics, might be anti-government, but I see anarchists as more left-wing.
The left wing is more authoritarian than the right, at least in a historical sense; thus, the right wing is close to anarchism. The Founding Fathers were probably considered close to anarchists in their day because their ideal government was only one step ahead of anarchy (i.e. as little government as humanly possible).
I'd actually expect someone to say that historically, the Left was more Libertarian than the Right.