It's not even an American sport.
IndyCar, LLC (the sanctioning body) is headquartered in Indianapolis, Indiana. It oversees the IndyCar Series (the premier championship) and the developmental Indy NXT series. The sport’s roots trace to early 20th-century American open-wheel racing, with “championship car” or “Indy car” competition dating back to around 1905 under the American Automobile Association (AAA). The Indianapolis 500, first run in 1911 at the Indianapolis Motor Speedway, has long been its centerpiece and one of America’s most iconic motorsport events (often called the “Greatest Spectacle in Racing”).
Key points supporting its American identity:
It developed as the U.S. counterpart to other forms of open-wheel racing (distinct from Formula 1).
Governing bodies have historically been American: AAA Contest Board, United States Auto Club (USAC), Championship Auto Racing Teams (CART)/Champ Car, and the Indy Racing League (which became IndyCar).
The vast majority of races are held in the United States (with occasional events in Canada, such as Toronto, and historically a few elsewhere).
Ownership is American (currently under Penske Entertainment Corp., which also owns the Indianapolis Motor Speedway).
It is affiliated with the FIA through the Automobile Competition Committee for the United States (ACCUS).
While the driver roster is highly international and the series has global appeal and occasional international races, the series itself, its history, primary venues, culture, and organizational structure are American. It is widely described as the premier category of professional automobile racing in the United States and the main form of American open-wheel car racing.
In short, IndyCar is to American open-wheel racing what NASCAR is to American stock-car racing: a distinctly U.S.-based motorsport tradition with deep national roots.