The Constitution gives Congress the sole responsibility of making war. The President is the Commander and Chief of the Armed Forces, but only Congress can declare war. In 1973, in reaction to President Johnson's use of executive war power, Congress limited the President's war power with the War Powers Act.
Article I, Section 8, clauses 12-16 of the Constitution state: "The Congress shall have power ... to declare war, grant letters of marque and reprisal, and make rules concerning captures on land and water; to raise and support armies, but no appropriation of money to that use shall be for a longer term than two years; to provide and maintain a navy; to make rules for the government and regulation of the land and naval forces; to provide for calling forth the militia to execute the laws of the Union, suppress insurrections and repel invasions; to provide for organizing, arming, and disciplining the militia, and for governing such part of them as may be employed in the service of the United States, reserving to the States respectively, the appointment of the officers, and the authority of training the militia according to the discipline prescribed by Congress."
The question of who gets to make war has been one of the most disputed questions between the Presdiency and and the Congress.The last time Congress declared war was in World War II. As far back as President Washington President have used their perogative as Commander of Chief to lead the army into war. There have been hundreds of times when the US military has been used without authorization. Since the Vietnam War, the war making powers of the Presidency have been limited by the War Powers Act, which required the President to notify the Congress when US troops were intruduced into areas of confilcts. the President has 60 days to act and another 30 days to pull out troops unless he receives Congressional authorization to continue the action.