The Constitution gives both the Congress and the President relevant power concerning the military. Congress rather than the president has the power to enact regulations for the armed forces and the power to declare war (Article 1 Section 8). But the President is the “Commander in Chief of the Army and Navy of the United States” (Article 2, Section 2). Charles Pinckney at the constitutional convention said that giving the President exclusive war power “would render the Executive a Monarchy of the worst kind.”
In practice, Presidents have dominated when it comes to war making. Consider this table:
Source: https://fas.org/sgp/crs/natsec/R42738.pdf
In the course of U.S. political history there have been only 5 declarations of war: 1812, 1846, 1898, 1917, and 1941.
Congress attempted to rebalance power in the War Powers Resolution which was enacted over President Nixon’s Veto in 1973. This effort has been at best only partially effective.