“This is just a more aggressive version of things campaigns are already doing,” said Zac Moffatt, who oversaw Mitt Romney’s digital strategy in 2012 and founded the firm Targeted Victory, which develops online campaigns. “You’ve got to break through,” he added, noting that guns would undoubtedly draw in potential voters who could be invaluable to a Republican candidate. “It could get you a couple extra thousand votes you didn’t otherwise know about.”

Lee Bright, a state senator from South Carolina who is challenging Senator Lindsey Graham in the Republican primary, has given away two guns, one online and one by direct mail. In the online drawing, the prize was an AR-15 rifle.

“We thought it was right in our wheelhouse,” Mr. Bright said. “We’re as strong Second Amendmentists as they come. And we wanted to reach out to like-minded folks.”

As a lot of candidates have learned, giving a gun away is not easy. First, the campaign has to make sure the winner is legally allowed to own a firearm. All those interviewed for this article said that background checks were being conducted through proper channels like licensed firearms dealers so a weapon did not fall into the wrong hands.

“You definitely don’t want to do that,” Mr. Bright said. “Not in the middle of the campaign.”

There is the issue of acquiring the gun, and if bought, making sure it is done through the proper channels. In Mr. Brophy’s case, the Smith & Wesson was donated by a supporter who is a firearms dealer. Under the law, Mr. Brophy has to report it on his campaign finance disclosure as an in-kind contribution. Other campaigns just buy the weapons. For its drawings, the N.R.A. said it relied on a combination of donated and purchased guns.

Then there is the issue of who is legally permitted to transfer the firearm to the winner. Campaigns are not licensed firearms dealers, so to make sure they are not making gun transactions illegally, many have opted to go through a gun store.

The task seemed so legally perilous that Joe Carr, who is challenging Senator Lamar Alexander of Tennessee in the Republican primary, hired a lawyer for his weapon sweepstakes.