Bah! Catholic priests that are married (and there are a few) are former married ministers from various Protestant denominations (primarily Anglican / Episcopalian) that were already married when they converted.
The history since VII is particularly long and boring. Operationally it works pretty much like this:
As an aside there is a "pastoral provision" which would provide "a common identity reflecting certain elements of their own heritage." Here an entire Episcopalian congregation could enter the Catholic Church and be allowed to remain a parish and use an Anglican-style Catholic Mass with either the traditional language of Archbishop Cranmer's
Book of Common Prayer or the modern English version. They would, however, submit to the Holy See on all matters etc etc etc. Since this is obviously, er, rare to non-existent the provision is extended thusly:
The Holy See has specified that this exception to the rule of celibacy is granted in favor of these individual persons, and should not be understood as implying any change in the Church's conviction of the value of priestly celibacy, which will remain the rule for future candidates for the priesthood from this group.
An ordained Episcopalian minister would make a profession of Faith and be received into the Catholic Church, and thereupon receive the Sacrament of Confirmation. He would then take appropriate courses which would enable him to minister as a Catholic priest (Holy Orders etc).
After proper examination by his Catholic bishop and with the permission of the Holy Father, he would be then ordained first as a Catholic transitional deacon and then as a priest. If the former Episcopalian minister were single at the time of his ordination as a Catholic deacon and then priest, he would indeed take the vow of celibacy. If the married former Episcopalian minister were ordained as a Catholic deacon and then priest, he would be exempt by a special favor from the Holy Father of making the promise of celibacy; however, if he later became a widower, then he would be bound to a celibate lifestyle and could not remarry. In the future, if a lay member of one of these reunited parishes wanted to become a Catholic priest, he would be required to take the promise of celibacy.
Further, the promise of celibacy is waived due to particular circumstances as a favor to those married clergy that wish to join the Church in a similar role based on their desire to reunite with the Catholic Church. This is, of course, confined to the Latin rite as outside of the US Eastern Rite Catholic priests are not require to be celibate (bishops are).
Posters above are correct in stating that celibacy is a discpline of the Church, not a doctrine. I believed this is confined to those that wish to become diocesan priests - not order priests. After Holy Orders I believe that they would merely become incardinated in their local diocese.
It is best to ask a Catholic about these matters.