Pursuant to the supreme law of our land, the U.S. Constitution, Senator Cornyn and Senator Sessions need to know this about any treaty we adopt:
This Constitution, and the laws of the United States which shall be made in pursuance thereof; and all treaties made, or which shall be made, under the authority of the United States, shall be the supreme law of the land; and the judges in every state shall be bound thereby, anything in the Constitution or laws of any State to the contrary notwithstanding.(US Constitution, Article VI, emphasis added). Even the constitutions and statutes of every state are made subject to foreign law when we put those laws into treaties, and the congress ratifies such treaties and the president signs them.
Thus The UN Ban on Torture and The Geneva Conventions are the supreme law of our land, and all state constitutions and judges are bound by that law, not merely instructed by it.
There are many, many treaties we have entered into over the years and we are none the worse for it, because it is wholesome to all nations who participate in dialogue to reach a mutual agreement for the good of many.