Army aviation pre-dates not just the Air Force, but the first flight of the Wright brothers. The US Army formed a balloon section in the Signal Corps in 1892, in 1898 the Board of Ordnance allotted $25,000 to Samuel Langley for his (ultimately unsuccessful) work on a heavier-than-air flying machine, and in 1907 the Signal Corps formally established an Aeronautical Division, generally recognised as the birth of the current Air Force. The Navy were a little slower off the mark, assigning a single officer to aviation matters in 1910 and funding the Bureau of Navigation in 1911 for experimental work, the first Marine aviator following in 1912.
Military aviation dramatically expanded with the First World War, in other countries this resulted in the establishment of Air Forces as independent branches (e.g. the Royal Air Force in the UK in 1918, merging the Royal Flying Corps of the Army and the Royal Naval Air Service). In the US aviation remained under the control of the other branches until after the Second World War; an Air Corps was established in the Army in 1926, becoming the US Army Air Force in 1941, but it was not until 1947 that the US Air Force was established as a separate branch of the armed forces (with Navy and Marine aviation remaining within those branches).
For further reading, see The United States Army Air Arm: April 1861 to April 1917, Juliette A. Hennessy, for early army aviation; Toward Independence: The Emergence of the U.S. Air Force 1945-1947, Herman S. Wolk, for the establishment of the independent air force; United States Naval Aviation 1910-2010, Mark L. Evans and Roy A. Grossnick, for naval aviation.