The picture has been shared more than 200 times.
It's been liked by more than 600 people and everyone is putting their 2 cents in.
Some are disappointed, others very forgiving of the officer, who appears to be sleeping while on duty.
ABC-7 asked Jennifer Ross, playing with her kids at the park, what she thought of the photo.
"Well, I think you have to take it in context. I mean obviously it's very shocking and awful and I would hope that our police aren't doing that," said Ross.
The officer is captured with his mouth open and the window slightly rolled down.
The person who uploaded the picture wished to remain anonymous.
The photo sparked a growing debate on the webpage among El Pasoans with hundreds of viewers leaving unfavorable comments about the pic.
Margarita Lugo posted commented on the Facebook picture.
"If he can't handle being on the job then maybe this job ain't for him. If anything happened u think he's going to b alert when he's dead asleep," wrote Lugo.
Celina Ontiveros wrote: "if people aren't allowed to sleep on the job anywhere else why is it ok for a officer in uniform in his patrol car? Umm go to bed at a decent time if you know you work the late shift or early morning. There is no excuse."
People ABC-7 spoke to on the streets had a more forgiving side.
"It's a concern, but that's just a photo. I mean I don't know if he just closed his eyes for a little bit or he was really asleep," said a man at Kern Park.
"I feel like most state jobs overwork our workers and they probably need some addressing how they compensate for a police officer's eight-hour or 16-hour day sometimes," said Cemelli de Aztlan who was at Kern Park.
But one Facebook post brought up a valid point.
Ricardo Hernandez wrote:
"The fact of the matter is he was on duty and armed. There is no good reason for him to be asleep"
"Police officers or anybody who's armed should not be asleep in a position where there weapon could be compromised," said another passer-by at the park.
"The fact that he is a trained officer (who)should be able to hold his weapon with some dignity and pride is definitely lacking in this picture," said de Aztlan.
ABC-7 contaced El Paso police spokesperson Michael Baranay and they sent us this statement:
"It is not acceptable for an officer to fall asleep while on duty. We will be conducting an administrative investigation and, in the event the officer was in fact asleep as it appears, the officer will be disciplined, wrote Baranay.
ABC-7 noticed the Facebook page "915 on blast" removed the picture from their page.
ABC-7 asked "915 on blast" why and they responded, "Because his friends asked us to."
The picture is still up on several other Facebook pages.