Sean Hillen, who lives in Bun na Leaca, said the signatures were collected over the last three weeks at a stand at the Falcarragh crossroads, and on line.
He said about 300 people who signed were from the island of Ireland, north and south.
The rest live in other countries, including the United States, Canada, France and Australia.
The petition states that Ireland requires leadership “of the highest moral level” from political and spiritual leaders.
”In allowing paedophile, Fr. Brendan Smyth, to remain at large and repeatedly abuse children and not inform parents or relevant authorities of the horrendous dangers, Cardinal Sean Brady, Primate of All Ireland, has failed to provide such leadership, has let people down and should voluntarily resign his position immediately,” the petition stated.
Mr. Hillen said he hopes a copy of the petition will be presented this week to a representative of the cardinal and to other groups, including Amnesty International Ireland and One in Four, the support group for people who were abused.
Mr. Hillen said he believed support for such a petition “had been building with each report on clerical abuse and what seemed to be the inaction, or at least not sufficient action, to investigate and deal with the issue — a kind of ‘pass the buck’ attitude”.
He said he believed the emotion reached a peak with the BBC broadcast earlier this month of Dara McIntyre’s report, “The Shame of the Catholic Church.”
The petition is on line at http://www.thepetitionsite.com/246/859/640/petition-calling-for-the-resignation-of-cardinal-sean-brady.