Jose Simms, 29, who is believed to be somewhere in New York, has seven arrest warrants and is being sought as a fugitive after failing to appear in court on a range of charges.
Brett Johnson of Torrington police in Connecticut posted on the department’s Facebook page on Wednesday that Simms had contacted him through the site and agreed to turn himself in if the post with his wanted poster racks up 15,000 likes.
Johnson said he negotiated Simms down from 20,000 likes.
“It will be difficult but is doable,” Mr Johnson wrote.
He also suggested that if anyone knows where Simms is hiding they could let police know and save the department some work.
At the time of writing, more than 20,000 users have liked the post, although police say he has not yet turned himself in.
The post will be updated if or when Simms turns up or is found.
'It turns this into a joke'
But Maki Haberfeld, an expert in police ethics and procedure at the John Jay College of Criminal Justice, said Simms was using social media to manipulate both the news media and police.
She said police have no business negotiating a deal with a suspect, never mind one that involves likes on Facebook.
“It turns this into a joke,” she said. “People will start looking at these various violations of law as a game.”
Simms, contacted through Facebook, said he is serious about the offer.
“I wanted to give them a little incentive for all the hard work they put in to catch me,” he wrote.
Simms said the charges stemmed from domestic problems and he was tired of running from authorities.
“Looking over your shoulder every five seconds can cause a lot of stress,” he wrote.
Simms said he is prepared to live up to his end of the agreement, insisting he is a “man of my word”.