It is an individual right but it's primarily a restriction on the Federal govt infringing the right. That was the new govt they feared.
“The power to declare war, including the power of judging the causes of war, is fully and exclusively vested in the legislature.” ~ James Madison, Father of the Constitution
“We do not believe in aggressive or preventive war. Such war is the weapon of dictators, not of free democratic countries like the United States.”~ Truman, Sept 1, 1950