Victoria Police posted a public appeal on Monday to locate Daniel Damon who is wanted for failing to answer bail for traffic and drug matters.
Damon replied to the post and to a number of other users commenting on the situation.
He told police he would turn himself in after getting things "organised".
"Can you use a better photo tho. This is a horrible mugshot," said Damon, 25, in response to the warrant.
"Hi Daniel, please visit your nearest police station and we'll arrange for a new photo to be taken!" police replied.
"Yea I plan on it once I get a few things in order... just gotta organise myself a lawyer and get everything organised," he said.
Police describe Damon as 180cm tall (5ft 11in), medium build, with brown hair and eyes and a fair complexion. He also has numerous body tattoos.
Senior Constable Melissa Seach told the BBC that police were making enquiries to locate him but he had not turned himself in.
She said police officer sometimes used social media as a tool as part of their investigation and it had led to good results in some cases.
"This may encourage someone that may know him to call us and provide information anonymously to crime stoppers," she said.
Damon's post was commented on by various people with some commending his sense of humour.
But most were keen on Damon being brought to justice.
"Yes think you may need that sense of humour where your going Danny boy," said Sue Hartley.
"This bloke is too arrogant for his own good," said Ajay Conodie.
"Victoria Police, he's not very good looking is he? Don't bother with any more photos," said Julie Benic Duck.
An Australian man is still at large after an exchange with police on Facebook where he asked them to change his mugshot.