Humberside Police advertised for the Â£117,078-a-year senior post on its website.
The Chief Constable said it was "vital candidates embraced new technology".
But a marketing expert has said the force should not have used "the tactic" for a very "serious role" that commands a degree of respect in the community.
Emma Pearson-Kendall, director of Fred Marketing, said: "You would hope in a role this serious people would take it seriously.
"I think it would be better maybe if they were saying this [area] was a great place to live and work and all the opportunities here, focusing on that rather than how the applicant looks."
Ms Pearson-Kendall said she hoped the selfie was not being used to "discriminate" against any potential candidates.
"I wouldn't do it and I probably wouldn't recommend that clients do it," she said.
Chief Constable Justine Curran said the force had "invested heavily in new technology in a bid to modernise the way we work".
She said: "We currently have a vacancy for a Deputy Chief Constable which is a key role within the force and as such it is vital that potential candidates understand the importance of embracing new technology within Humberside Police at the point of applying for the role.
"This is why we have created a recruitment advert that reflects our aims and ambitions as a force by encouraging candidates to get involved from the outset."

The 56-year-old was sacked by Chester in April after a run of just one win in 10 put the club in a relegation fight.
Southport relieved Andy Bishop of his duties on Saturday with the side lying second from bottom in the table.
Ex-Kidderminster boss Burr takes over a side that has picked up four points from their first eight league matches of the season, suffering six defeats.

The collapse took place very close to the famous Ponte Vecchio, a medieval covered bridge over the Arno.
The hole is about 200m (650ft) in length and 7m (23ft) across.
Firefighters believe the chasm has been created by the failure of a large water pipe beneath the surface.
Florence's Mayor Dario Nardella tweeted (in Italian) that no-one had been harmed in the incident on Lungarno Torrigiani.
He appealed to motorists to remove their cars from the nearby area, and said the water supply to part of the city centre was cut off.
Regional paper Corriere Fiorentino reports that thousands of residents are without water.
The first sign of the problem came not long after midnight, when the police were called, the mayor told Italy's Ansa news agency.
The major collapse took place at 06:14 local time, Mr Nardella said.
A police force recruiting for a new deputy chief constable has requested applicants submit a "selfie" in order to apply for the role.
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National League side Southport have named former Chester boss Steve Burr as their new manager.
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A section of the embankment of the River Arno in central Florence collapsed on Wednesday morning, sending part of the road and at least 20 parked cars into a newly formed ditch.