The survey, conducted by GOP firm Harper Polling, gives Rounds a 14-point lead over Weiland, with 52 percent support to Weiland's 38 percent support.
Rounds is a well-liked former governor and entered the race with establishment backing, but conservatives are unhappy with his record and have pledged to issue a strong primary challenge.
So far a number of contenders have already entered the primary, including state Rep. Stace Nelson, state Senate Majority Whip Larry Rhoden and physician Annette Bosworth. But according to the new poll, none are as competitive as Rounds against Weiland.
Both Rhoden and Nelson still lead Weiland, but by smaller margins. Rhoden takes 41 percent to Weiland's 35 percent support, while Nelson leads the Democrat by only two points.
And Weiland actually leads Bosworth by two points.
Overall, the atmosphere is favorable for a Republican in South Dakota. In a generic Senate matchup, 46 percent of respondents would vote for a Republican, while 36 percent would back a Democrat. And 54 percent disapprove of President Obama's job performance.
The survey was conducted among 517 likely voters from Sept. 4-5, and the margin of error is plus or minus 4.3 percentage points.