No, the Federal Aviation Administration was not a New Deal program. In fact, the FAA was not created for decades after the end of the New Deal. To be specific, the FAA was not created until Congress passed the Federal Aviation Act of 1958.
During the New Deal era, aviation was regulated by the federal government. At that point, there was an entity known as the Aeronautics Branch (created in the 1920s) that operated as part of the Department of Commerce. The Aeronautics Branch was in charge of regulating civilian aviation. However, the FAA itself was not created until much later.