Cardinal Keith O'Brien said many priests struggle to cope with celibacy and should be able to marry and have a family.
The cardinal was speaking ahead of a trip to Rome where he will help elect the next pope, after the resignation of Benedict XVI.
He told the BBC: "I'd be very happy if others had the opportunity of considering whether or not they could or should be married.
"It's a free world and I realise that many priests have found it very difficult to cope with celibacy as they lived out their priesthood, and felt the need of a companion, of a woman, to whom they could get married and raise a family of their own."
Cardinal O'Brien, 74, stood down from some frontline duties in the Catholic Church in Scotland last year due to his age.
He quit the position of Bishops' Conference of Scotland, the key decision-making body in the church.
He said that marriage was not considered when he was studying for the priesthood but added he would be happy to see it introduced.
Cardinal O'Brien added: "I would like others to have the choice. In my time there was no choice, you didn't really consider it too much.
"It was part of being a priest when I was a young boy, priests didn't get married and that was it.
"When you were a student for the priesthood, well it was part of the package, as it were, that you were celibate, that you didn't get married and you didn't really consider it all that much, you just took your vows of celibacy the way someone else would naturally take their vows of marriage."
Cardinal O'Brien welcomed Pope Benedict when he visited Scotland in 2010.
He has been an outspoken opponent of Scottish Government plans to legalise same-sex marriage and was controversially named "bigot of the year" by a gay rights charity last November.
Stonewall said he was given the title because he went "well beyond what any normal person would call a decent level of public discourse" in the debate.
The Catholic Church criticised the charity's award, saying it revealed "the depth of their intolerance" and a willingness to demean people who do not share their views.