The Department of War, which included the armed forces, was part of the executive branch during the early years of the Republic. Which article of the Constitution empowered the executive branch to create the department?

It is Article II, Section 3.

Explanation:

Article II of the Constitution defines the Office of the President, its duties, powers and other aspects. In Section 3, the Constitution enumerates some presidential prerrogatives. Among other things, it says that the president "shall commission all the Officers of the United States."