His lawyers argued that a shorter statute of limitations on child sex crime prosecutions should have applied to offenses dating back to the 1990s.
The justices did not detail their reasoning in declining to hear the case, as is typical. Lower courts previously rejected his arguments.
Federal prosecutors have said the video showed Kelly abusing a girl. The accuser identified only as Jane testified that she was 14 when the video was taken.
Kelly has also appealed a separate 30-year sentence for federal racketeering and sex trafficking convictions in New York.