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).
The left-wing, in the historical sense, advocates for radical if not revolutionary change, whereas the right-wing advocates for gradual change if any at all. With that in mind, most anarchists throughout history have identified with the left-wing, even though many totalitarians have also done so. To say that anarchism is of the right-wing has little or no basis in reality outside of the American political paradigm.