Again, the Catholic encyclopedia comes to the rescue......
Present Position With regard to the law of celibacy and its canonical effects in the Western Church at the present day, only one or two points can be briefly touched upon. For the details the reader must be referred to such a work as that of Wernz "Jus Decretalium", II, 295-321.
Clerk in minor orders, as already stated, as free to marry, and by such marriages they forfeit the privilegia canonis and the privilegia fori only in part, provided they observe the required conditions (cf. Decreta Conc. Trid., Sess XIII, cap. vi); though in our day such observance is practically impossible;
but they are incapable of being promoted to sacred orders unless they separate from their wives, and make a vow of perpetual continence. Further, if as clerks they held any
benefice or ecclesiastical pension, these are at once forfeited by marriage, and the become incapable of acquiring any new
benefice. Historically there has been some little variation of practice with regard to married clerks, and the severe measures enacted in their regard by
Pope Alexander III were subsequently mitigated by
Boniface VIII and the
Council of Trent. As regards ecclesiastics in sacred orders (i.e. the subdiaconate and those that follow), the teaching of both theologians and canonists alike, for many centuries past, has been unanimous as regards the facts, though some little divergence has existed regarding the manner of explaining them. All are agreed that the subdeacon in presenting himself of his own free will for ordination binds himself by a tacit vow of chastity (Wernz, IV, n. 393), and that this even constitutes a diriment impediment in view of any subsequent marriage. The idea of this votum annexum seems to be traceable in one form or another as far back as the time of
Gregory the Great. Although the opposition to the law of celibacy frequently took the form of open agitation, both in the earlier
Middle Ages and again at the Reformation period, only one such movement calls for notice in modern times. This was an association formed principally in Würtemberg and Baden in the early part of the nineteenth century to advocate the mitigation or repeal of the law of celibacy. The agitation was condemned by an Encyclical of
Pope Gregory XVI, on 15 August, 1832, and no more permanent harm seems to have resulted than the publication of a certain amount of disaffected literature, such as the pretentious but extremely biased and inaccurate work on compulsory celibacy by the brothers Theiner, a book which at once prohibited by authority and repudiated by Aug. Theiner before he was reconciled to the Church.
i don't know if it's 'allowed' or not but i do know tht not all rites within the Catholic Church deny the right to marry as priests.
