The short answer is no. The longstanding and fruitful discipline of the Latin or Roman Catholic Church is that celibate men are ordained as Priests and once a man is ordained as a Deacon or a Priest he cannot get married. In the case of Permanent Deacons a married man can be ordained as a deacon and in special circumstances a married man may be ordained as a Catholic priest. Among the special circumstances is the case of a married man who had been ordained as an Anglican or Lutheran minister when he becomes a Catholic, with special permission, may be ordained as a Catholic priest. Another special circumstance is the Personal Ordinariate of Our Lady of the Southern Cross. The personal ordinariate is for groups of Anglicans in Australia who desire full communion with the Catholic Church while retaining some Anglican liturgical traditions. On a case by case basis, with the judgement made at the Vatican, married Anglican ministers who are members of the group seeking to join the Catholic Church may seek to be ordained as Catholic priests.
In the Eastern Catholic Churches, such as the Maronite or Ukrainian Catholic Churches, a different discipline has been in force for many centuries. In Eastern Catholic Churches bishops are chosen solely from among celibates. Depending on local circumstance, married men can be ordained as deacons and priests.
Returning to the short answer, in ordinary circumstances a Catholic priest is not allowed to marry.
In 2019 Pope Francis affirmed the dignity and fruitfulness of celibate priests, “I think that celibacy is a gift to the Church… I would say that I do not agree with allowing optional celibacy…”
Blue sky photo by Xavier Coiffic on Unsplash
14 October 2019