Riverton, New Jersey. Riverton is a borough located in Burlington County, New Jersey, United States. As of the 2010 United States Census, the borough had a total population of 2,779, reflecting an increase of 20 (+0.7%) from the 2,759 counted in the 2000 Census, which had in turn declined by 16 (-0.6%) from the 2,775 counted in the 1990 Census.