Can white people have black hair?

Yes.

Lots of White people have Black hair.

Take a look at some of your favorite celebrities such as Elvis Presley, Robbie Williams, Bono, Andrea Corr, Joey Ramone, Joan Jett, Hugh Jackman, Sylvester Stallone, Bruce Campbell, Michael Keaton, Michael Madsen, John Travolta, John Cusack, Jack Nicholson, Catherine Zeta-Jones, Megan Fox, Joseph Gordon-Levitt, Colin Farrell, George Clooney, Johnny Knoxville, etc.

Even some of your childhood superheroes have Black hair.

Like Superman, Wonder-Woman or Snow-White.

Black hair is common among Whites.

Caucasian people can have any color of hair, including black. But so can any other race, but it's rarer. The three distinct hair colours are Blond, brown, and Black, red being a type of blonde. In the same way it is rare for a white person to have the wooly, afro-textured hair of a Negro, despite living in cold regions of the world.