The United States was not one of the original signers of the 1982 United Nations Conventions on the Law of the Sea. In 1994, it was signed by the President and transmitted to the Senate for ratification. As of 2016, the full Senate has yet to vote on the treaty.
The U.S. State Department's Brief History of U.S. Efforts Relating to the Law of the Sea provides a chronology, along with links to relevant documents, including:
Congress.gov provides a chronology of Senate consideration, and congressional hearings and statements are also available from the Senate Committee on Foreign Relation's page, 103-39: United Nations Convention on the Law of the Sea.
The U.S. State Department also publishes an annual compilation, Digest of United States Practice in International Law.
Various federal agencies, departments, bureaus, and offices have Law of the Sea and related issues as part of their mission.