In the Stargate universe the Stargate program is run by the United States Air Force. But why was the Air Force given the reins on this project? Is it simply because the Stargate was located in Cheyenne Mountain, which also houses the Cheyenne Mountain Air Force Station? Or is there an alternate reason, in or out of universe, for why the Air Force was chosen over another branch of the United States Armed Forces or the Canadian Forces that make up the combined Cheyenne Mountain Directorate?
The United States Air Force has a unified Space Command and the headquarters for that particular division is fairly close to Cheyenne Mountain. In particular, you have the Fourteenth Air Force which is the space war fighting arm of the United State military.
The cryptoanalysis branch of the Air Force is now called the Air Force Intelligence, Surveillance and Reconnaissance Agency. They report to the Space Command. Given that this thing they found is made of exotic materials and covered with alien symbols, I'd think they'd want to take a look at it.
Also given that when the Stargate was discovered the Army and the Air Force were the same branch, it seems reasonable to assume that it simply got transferred to the Air Force when the two branches were separated. Particularly given that the Signal Corps were the origin of the Air Force.