[The President] shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur;
(US Constitution, Article II, Section 2, Clause 2)

The Constitution gives rolls to both the executive and legislative branches for the making of treaties. The rational for this was to provide a check on the treaty making process. By requiring a super majority of two-thirds in the Senate to agree to the treaty the Founders believed that more deliberation and thought would be put into the making of a treaty than common law. They also believed that by having the Senate consent to the treaty a small majority would be prevented from making treaties. (The smaller states had equal representation with the larger states in the Senate.) The House was too large in the minds of the Founders to be involved in making a treaty, this body would have difficulty keeping secrets or acting quickly.