Writing in her blog, Sinead O’Connor said she wanted to join the party “just as a regular punter” because she wanted to see a “proper socialist Ireland”.
However, in a Facebook post on December 8, the singer also called for the Sinn Féin leadership to step down.
A Sinn Féin spokesperson said the party welcomed her membership application and that it was currently being processed.
Sinead O’Connor achieved worldwide fame in 1990 with the song Nothing Compares 2 U, written by Prince.
She has often courted international controversy over her outspoken political and religious views.
Sinead O’Connor currently writes a regular blog on her website, entitled Sinead’s musings.
In recent weeks, the singer’s posts have focused on the controversial introduction of domestic water charges in the Republic of Ireland and the legacy of the 1916 Easter Rising, the rebellion against British rule.
In her latest blog entry, entitled Strange Week, Sinead O’Connor wrote: “I’m joining Sinn Féin now. If they’ll have me.
“Just as a regular punter who wants to learn and contribute with whatever strengths I might have or learn. I’d like to see a proper socialist Ireland.”
She also said that she has “never voted” in an election in her life.
Writing in a later Facebook post on Monday night, Sinead O’Connor said she “might not even be the kind of person they [Sinn Féin] want”.
She added: “I feel the elders of Sinn Féin are going to have to make ‘the supreme sacrifice’ and step down shortly in the same way the last Pope did.”
Both Sinn Féin and the hierarchy of the Catholic Church have faced criticism over how they dealt with allegations on child abuse in Ireland.
It is not the first time Sinead O’Connor has publicly criticized Sinn Féin or other political parties.
In a blog entry last week, dated December 1, she wrote: “We have a system left over from 1922. Fine Fail (sic)/Fine Gael/Sinn Fein, all of them. They are of the old order. They are of our violent history.
“We need new politics. Young people. Not people of the theocracy. Not people of “The War”. Not of any war.”
In a statement to the Journal.ie news website, a Sinn Féin spokesperson said: “We look forward to working with Sinead as part of Sinn Féin delivering change in communities across Ireland.”
However, the party later defended its leaders against the singer’s calls for them to step down.
“The membership of the party selects the Sinn Féin leadership every year at our Ard Fheis [the party’s annual conference],” a spokeswoman said.
“As a member, Sinead would have an equal say in that process.”
It also said that support for the party in the Republic of Ireland “has grown considerably” since Gerry Adams was elected as a member of the Irish parliament.
Sinead O’Connor has a history of hitting the headlines over issues unrelated to her music career.
In December 2011, Sinead O’Connor annulled her fourth marriage to therapist Barry Herridge 16 days after their wedding.
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