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."
A police force recruiting for a new deputy chief constable has requested applicants submit a "selfie" in order to apply for the role.