This has got to be one of the oddest promotions to involve NFL players — no ifs, ands or, er, butts.

Four NFL linemen have signed to help a small Venice, Calif., company crack a new market — moistened toilet paper — targeted at men.

The sector, just 3 percent of the $8.7 billion toilet paper category, is usually aimed at infants and toddlers but the four burly centers are hoping to change that with a product cheekily called “One Wipe Charlies.”

The players — the Dallas Cowboys’ Travis Frederick , the Minnesota Vikings’ John Sullivan, the Buffalo Bills’ Eric Wood, and the San Diego Chargers’ Nick Hardwick — will be part of a marketing blitz, entitled “Clean Snap,” to kick off in two weeks.

It’s the brainchild of Mike Dubin, CEO of Dollar Shave, who told The Post: “Most of the centers we approached were game to try this. They are guys not a lot of people are reaching out to. ”

“We wanted to make something just for men; it’s aspirational: a way to get it done in one,” Dubin said.

A survey conducted by Dollar Shave found that 89 percent of wipe users were very satisfied with the cleanliness of their butt after using a wipe — versus only 58 percent for traditional TP.

“I’ve been using wet wipes for years,” said Dubin, “Its an enjoyable experience.”

Financially, the players are far from cleaning up with the deal. They are likely pocketing only $10,000 or so for the campaign, according to Advertising Age, which first reported on the deal.

Dubin is expected to be part of an Advertising Week session next week on gutsy startups, called: “Balls of Steel.”