The answer is murky because of a split between the apparent intent of the Constitution and how the country has been governed in practice. Most legal scholars agree that the founders wanted Congress to decide whether to go to war, except when the country is under an attack. But presidents of both parties have a long history of carrying out military operations without authorization from Congress, especially since the end of World War II, when the United States maintained a large standing army instead of demobilizing.
In the modern era, executive branch lawyers have argued that the president, as commander in chief, may use military force unilaterally if he decides a strike would be in the national interest, at least when its anticipated nature, scope and duration fall short of a war in the constitutional sense, as a Clinton administration lawyer wrote in the context of a contemplated intervention in Haiti.