Dr Desmond Connell was among 37 senior clergymen who received the honour at an open air ceremony in the Vatican on Wednesday.
The Irish Prime Minister Bertie Ahern attended the installation, which had to be moved outside to St Peter's Square, because of the demand for places.
Cardinal Connell said afterwards: "It's a glorious day, a very joyful day, in which so many people are involved.
"I suppose the honour comes to the one at the top, but it should be shared and is shared by all those who are representing me.
"I thanked the Pope and I thanked him on behalf of Ireland."
Dr Connell, 75, is the first bishop of Dublin in 116 years to have the honour of cardinal conferred upon him.
Usually it is reserved for the Archbishop of Armagh - the leader of the Catholic Church in Ireland.
That position is currently held by Archbishop Sean Brady.
Religious commentators say Dr Connell's appointment is an unusual step which will raise questions about where power lies in the church in Ireland.
Dr Connell this week angered Church of Ireland bishops with remarks about Catholics receiving communion at Protestant church services.
He was first involved in controversy over the issue three years ago, when Irish President Mary McAleese took communion at a Church of Ireland cathedral.
Communion comments
He said then Anglican ministers who welcomed everyone to communion were failing to respect the faith and obligations of Catholics.
He repeated his views at the weekend in an interview for the Sunday Business Post newspaper.
On Monday the leader of the Church of Ireland, Archbishop Robin Eames, said it was "tragic" that communion was being viewed as a source of division.
Dr Connell's remarks drew stronger criticism from Dublin's Church of Ireland Archbishop, Dr Walton Empey.
Dr Empey said he was saddened Dr Connell's elevation, which could have been a joyful one for the Catholic Church, was being marred by "acrimony".