http://www.washingtonpost.com/blogs/wonkblog/wp/2014/12/22/a-lot-of-southern-whites-are-a-little-bit-black/ suggests 3.5% of self-described white Americans have at least 1% black ancestry, but it is significantly higher in some states like South Carolina and Louisiana. http://www.theroot.com/articles/history/2014/03/how_many_white_people_have_hidden_black_ancestry.html is another article on the subject. So is http://www.nytimes.com/2014/12/25/science/23andme-genetic-ethnicity-study.html . They all seem to come from http://blog.23andme.com/23andme-research/dna-usa-2/ .
Of course, “some” black ancestry could be less than 1%, so the percentage would be higher with a lower threshold than 1%.