"International law consists of 'rules and principles of general application dealing with the conduct of states and of international organizations and with their relations inter se, as well as with some of their relations with persons, whether natural or juridical.' While the United States has long understood international legal commitments to be binding upon it both internationally and domestically since its inception, the role of international law in the U.S. legal system often implicates complex legal principles. The United States assumes international obligations most frequently when it makes agreements with other nations or international bodies that are intended to be legally binding upon the parties involved. Such legal agreements are made through treaty or executive agreement. The U.S. Constitution allocates primary responsibility for such agreements to the executive branch, but Congress also plays an essential role. First, in order for a treaty (but not an executive agreement) to become binding upon the United States, the Senate must provide its advice and consent to treaty ratification by a two-thirds majority. Secondly, Congress may authorize executive agreements. Thirdly, the provisions of many treaties and executive agreements may require implementing legislation in order to be judicial enforceable in U.S. courts."
CRS Report for Congress, RL32528
Congressional Research Service: https://crsreports.congress.gov/