That is true, Seruzawa. Article 2, Section 2 of the Constitution states:
He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur;
http://www.usconstitution.net/const.html#A2Sec2
DTogo is correct about Article 6 concerning treaties, once signed by the President and ratified by the Senate, become the law of the land. Article 6 link:
http://www.usconstitution.net/const.html#Article6
and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land;