It's one of those patented Paul passages where Paul tries to please all sides. The chapter opens with Paul trying to make nice with the Roman authorities (who at the time of the epistle haven't quite figured out what this new cult out of Palestine is all about, and haven't begun to oppress it) : "Let everyone be subject to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. Consequently, whoever rebels against the authority is rebelling against what God has instituted, and those who do so will bring judgment on themselves."
It's a favorite passage for folks in power: I'm running things because God put me here. Don't oppose my authoritah or it'll go bad for you, and you'll deserve it.
Oddly, though, the die-hard supporters of the former guy and his fucked-in-the-head party tend to overlook much of the rest of the chapter. Beginning at verse 6: "This is also why you pay taxes, for the authorities are Gods servants, who give their full time to governing. Give to everyone what you owe them: If you owe taxes, pay taxes." Maybe Paul should have laid down divine marginal tax rates?
Anyway, it's that "governing authorities are ordained by God" notion that provides the jumping-off point for bad government to justify its oppressive policies.