South Australian Greens senator Sarah Hanson-Young says a crude Facebook post shared by a business owned by Ceduna's Mayor is "degrading" to women.

Key points: Ceduna Boat Charter shared a social media post about Greens senator Sarah Hanson-Young

Ceduna Boat Charter shared a social media post about Greens senator Sarah Hanson-Young Mayor Perry Will says his Facebook page was hacked

Mayor Perry Will says his Facebook page was hacked Senator Hanson-Young is considering making a complaint

She said the post, a meme about ribbed condoms which included her picture, was revolting and that Mayor Perry Will should be setting an example for his town.

Mr Will, who owns Ceduna Boat Charter, told the ABC that his Facebook account had been hacked.

However, Senator Hanson-Young said the post was up for 10 days and was commented on by family and friends.

"Frankly, I'm not going to sit by and be a punching bag for people who think degrading women is funny," she said.

"It's not, it's wrong."

She said she was considering making a complaint that Mr Will had breached the local government Code of Conduct for Council Members.

The code stipulates that elected members must act in a way that "generates community trust and confidence in the council" and "show respect for others if making comments publicly".

The post was shared from a far-right Facebook page called "National Uprising".

The ABC has seen the post but has chosen not to publish it.

"It was degrading not just to me but to all women and something that just should never have been shared by a person in public office and frankly it says a lot about whether Mr Will is appropriate to be an elected mayor," Senator Hanson-Young said.

Mr Will defended by former Ceduna mayor

Mr Will was elected in November 2018 by five votes.

Ceduna Mayor Perry Will. ( District Council of Ceduna )

He told ABC Eyre Peninsula host Emma Pedler off air that his Facebook page had been hacked and that he was trying to delete the post yesterday but found it difficult because of the Facebook outage.

He has since deleted his Facebook page.

Mr Will did not answer his phone this morning after agreeing to an interview on radio.

Former Ceduna mayor Allan Suter said the post was "totally unlike anything Perry would do" and he believed that his Facebook account was hacked.

He said the behaviour of people on social media in Ceduna recently had been "totally horrendous".

"Perry's been subjected to rude, defamatory, insulting content and the sorts of people who are capable of that sort of behaviour are capable of hacking into a webpage," Mr Suter said.

Senator Hanson-Young said she had received no apology or explanation from Mr Will and his account being hacked seemed "highly convenient".

Ceduna is a beachside town on South Australia's far west coast. ( ABC News: Nicola Gage )

Ceduna divided over oil drilling

The Ceduna community has been divided recently over whether or not to allow Norwegian oil company Equinor to drill for oil in the Great Australian Bight.

A trial of the cashless welfare card in the town has also split the community.

Mr Will is in favour of drilling and of the cashless welfare card, while the Greens are opposed to both measures.

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Penong resident Trina Spitzkowsky, who has been involved in the Fight for the Bight campaign, said Mr Will's post was "disgusting".

"I'm incredibly disappointed that somebody in that position could think like that," she said.

She said he should apologise publicly or step down from his position "if he's going to carry on like that".

"It's the year 2019 and we don't tolerate this sort of behaviour any more," she said.

Senator in defamation case

Separately, Senator Hanson-Young launched legal proceedings against former Liberal Democrat senator David Leyonhjelm last year, accusing him of attacking her character in a media statement and subsequent interviews.

She claims Mr Leyonhjelm suggested she was a misandrist and a hypocrite and that he repeatedly falsely accused her of claiming that all men were rapists.

He denies defaming her.

She is vying for re-election at this year's federal election, expected to be held in May.