There's no single date for the invention of the car in the US. Several inventors contributed to its development over time. However, Karl Benz's invention of the first practical automobile in Germany in 1886 is generally considered a crucial starting point. American inventors then built upon this, improving and adapting the automobile for American roads and needs.
So, there's no year we can definitively say the car was "invented" in the US. Instead, it was a process of innovation with many contributors.