The executive branch of the U.S. government is the primary agent of foreign policy.
However, Article I gives Congress the authority to regulate foreign commerce (i.e. tariffs)
Article II of the Constitution gives the president the authority to make treaties (with the consent of Senate) and to appoint & receive (recognize) ambassadors
The president is advised by:
Secretary of State (State Department)
National Security Council (NSC) est.1947
Joint Chiefs of Staff (Pentagon)