You may be thinking about Wendell Scott, who was the first (and to date, only) African-American driver to win a NASCAR race, the 1964 event at Speedway Park in Jacksonville, Florida.
Exact records are unclear, but he is believed to be the first African-American to obtain a NASCAR license. In his book, Hard Driving: The American Odyssey of NASCAR's First Black Driver, Brian Donovan chronicles Scott's career as a driver.
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There has never been an African-American F-1 driver
The question does not mention nationality, just ethnicity, and even then the above answer is incorrect.
William Theodore Ribbs Jnr, drove an F1 car for Brabham in 1986, although he did not compete in any races.
Lewis Hamilton (of mixed descent) has been racing in F1 since 2007
To date, I don't think there's been one. However, the first woman to drive in NASCAR was Janet Guthrie, and the first black man to drive was Wendell Scott. You see, there is no Formula One for women.
On June 10, 2007, Lewis Hamilton won the Canadian Grand Prix, becoming the first black driver to win a Formula 1 race. He was born in Stevenage, Hertfordshire, England.
In 2008, Hamilton won the Formula 1 World Championship.
Narain Karthikeyan is the first Indian Formula One driver. He has raced for Jordan (2005) and HRT (2011 and 2012).