It is not part of the US Constitution.
ORLY? Check out Article I, Section 8, Clause 10 'Law of Nations'
The full title of Vattel's work was the The Law of Nations or the Principles of Natural Law, and it was what the Founders used to WRITE the Constituion.
Not only in an UNoffical capacity-
I am much obliged by the kind present you have made us of your edition of Vattel. It came to us in good season, when the circumstances of a rising state make it necessary frequently to consult the law of nations. Accordingly, that copy which I kept, (after depositing one in our own public library here, and sending the other to the college of Massachusetts Bay, as you directed has been continually in the hands of the members of our congress, now sitting, who are much pleased with your notes and preface, and have entertained a high and just esteem for their author. Your manuscript Idee sur le gouvernment et la royauté, is also well relished, and may, in time, have its effect. I thank you, likewise, for the other smaller pieces, which accompanied Vattel.
Benjamin Franklin To Charles-Guillaume-Frédéric Dumas, Philadelphia December 9, 1775.
but also in an OFFICAL capacity as well-
Journal of the Senate of the United States of America / Monday / March 10, 1794 / Volume 2 / page 44
Ordered, That the Secretary purchase Blackstone's Commentaries, and Vattel's Law of Nature and Nations, for the use of the Senate.
Even after Ratification, legal scholars continued to state the importance of Vattel's work within the mechanics of Constituional Law.
It will he remembered, that the object of the several states in the adoption of that instrument, was not the establishment of a general consolidated government, which should swallow up the state sovereignties, and annihilate their several jurisdictions, and powers, as states; but a federal government, with powers limited to certain determinate objects; viz. their intercourse and concerns with foreign nations; and with each other, as separate and independent states; and, as members of the same confederacy: leaving the administration of their internal, and domestic concerns, to the absolute and uncontrolable jurisdiction of the states, respectively; except in one or two particular instances, specified, and enumerated in the constitution. And because this principle was supposed not to have been expressed with sufficient precision, and certainty, an amendatory article was proposed, adopted, and ratified; whereby it is expressly declared, that, "the powers not delegated to the United States by the constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people." This article is, indeed, nothing more than an express recognition of the law of nations; for Vattel informs us, "that several sovereign, and independent states may unite themselves together by a perpetual confederacy, without each in particular ceasing to be a perfect state.
Of the Unwritten, or Common Law of England; And Its Introduction into, and Authority Within the United American States
Just because we have been told all our lives by our government educators that the federal government is the sole arbitrator of what the Constitution MEANS doesn't make it true.