"The international law to which you are referring is the Paris Declaration of 1856, which the United States never signed or ratified."
If you finish reading the Wikipedia article, where you obviously found it, you'll notice that, despite not being a signatory, the United States abides by the terms of the treaty. There are several types of international law, one of which is called "customary international law." These are things which, while not necessarily part of a treaty a state has signed, are widely acknowledged as binding international law and held in equal weight with law created by treaties, unless there is a conflict. Then the treaty terms win. For example, it was customary international law not to harm diplomats long, long, before the Vienna Convention codified it in the 1960s. Privateering is firmly against customary international law, so it matters not that we aren't a party to this specific treaty.
"Yeah, but I'm referring to Letters of Marque AND Reprisal, not a simple letter of marque. Consider terrorists to be air pirates and take them out with letters of reprisal."
The "reprisal" part just authorizes the individual to cross an international border to achieve the end. What this means is that you can go into a state's internal waters or even a port rather than just operate on the high seas. It doesn't mean "reprisal" as in revenge. Legal terms rarely have the same meaning as the colloquial definition of the word.
As for them being air pirates (assuming that's even a legitimate category, which it probably isn't), how does this affect anyone not involved with airplane hijacking? The terrorists in, say, Benghazi couldn't be connected with that.
I'm familiar with the Ron Paul argument here. In the specific period after 9/11 it might just have made sense and been a decent policy alternative. I don't see how glorified Dog the Bounty Hunters are better than the US military in attackign terrorists, but I'm willing to be convinced it may have worked then. But it certainly wouldn't now, even excluding the illegality of privateering.
As I said, you're really advocating for bills of attainder. Those can't be done. You're just attaching yourself to an obsolete scrap of the Constitution that sounds steam-punk and sexy and bending reality to make your argument sound plausible. It isn't.