Both the Army and Marines operate their own rotary wing aircraft, but only the Marines operate their own fixed wing aircraft too
It should be noted that every time the Army tried to get its own fixed wing aircraft for ground support, the Air Force blocked the move.
And the only reason the Air Force doesn't do the same to the Marines is that the Marines are NAVY. And the Navy never let the Air Force camel's nose into their tent.
For those who aren't big on inter-service rivalry history, this all grew out of the squabbling between the Bomber Generals and everyone else in the WW2 Army Air Corps.
The Bomber Generals believed that the Army (and Navy) were no longer necessary, because any enemy could be defeated by just bombing him into oblivion. They didn't even see a burning need for fighters, since the massed bombers could defend themselves nicely.
After WW2, when the Army Air Corps started pushing for their own branch of service (US Air Force), they very conveniently overlooked things like the Schweinfurt Raid (bombers only, no fighter escort, since the P47 and P51 weren't ready, lots of bombers didn't come home. Not quite a majority didn't come home, but it was close), and demanded control of ALL fixed-wing aviation. The Navy told them to f**k off, but the Army was forced to give it all up.
Since then, every time something new that could fly came along, the Air Force has tried their best to make sure it was forbidden to the Army. They failed with helicopters, but they've always succeeded with armed fixed wing planes....