An earlier poll by the same group, conducted on April 17, found the race tied at 38.5 percent each.
Cotton has been up on local TV with some strong biographical ads, which may explain his movement in the poll.
He also has the backing of the GOP establishment in Washington, D.C.
Conservative Democrat Rep. Mike Ross is retiring, leaving the seat open this cycle.
If Cotton is the GOP nominee in the district, Republicans are likely to pick up the seat in November. The primary is May 22.
Both polls were conducted using interactive voice response technology, also known as robopolling. That technology, while substantially cheaper than traditional live-interview polling, can introduce significant error into polls because, among other reasons, IVR polls don’t survey cellphones. That means the poll misses the many households that don’t have a land line telephone. Still, some IVR polls have been shown to be as accurate as live-telephone polls in the days before an election.
The May 10 poll surveyed 437 likely Republican voters in the district. It had a margin of error of 4.7 points. The April 17 poll surveyed 542 likely Republican voters in the district and had a margin of error of 4.2 points.