The letters of marque and reprise clause of the US Constitution was superceded by a treaty banning such in the 1860s I believe.
Prior to the US Civil War there was an effort by the major maritime states to ban or restrict letters of marque and reprise, an effort that was resisted by the US at the time. The US position was based on the US not having much of a Navy, privateers could be a useful augmentation to US naval power.
Following the US Civil War and coincident with technological developments that made privateers mostly moot (armored warships, steam power, rifled cannon firing exploding shells) and the Union experience of Confederate commerce raiders, the US position changed and she adhered to the treaty.
I still want to be a privateer.
Treaties CANNOT override the Constitution. The power to make treaties was given to the President by the People, in the Constitution. The power to ratify treaties was given to the Senate by the People, in the Constitution. The Constitution can only be changed by the People, acting through 3/4 of the state legislators, or via state delegations to a 2nd Constitutional Convention (the latter of which is, at present, only theoretical, as a 2nd one has never been called...and I hope it never is).
In short, the creator cannot be overridden by the created. Treaties can be found unconstitutional - what would you think of a treaty that revoked equal rights for women and all non-Muslims, and which instituted Sharia Law as the supreme law of the land?