Objection 1. It would seem that a man ought not to be debarred from receiving Orders on account of a lack of members. For one who is afflicted should not receive additional affliction. Therefore a man ought not to be deprived of the degree of Orders on account of his suffering a bodily defect.
Objection 2. Further, integrity of discretion is more necessary for the act of orders than integrity of body. But some can be ordained before the years of discretion. Therefore they can also be ordained though deficient in body.
On the contrary, The like were debarred from the ministry of the Old Law (Leviticus 21:18, seqq.). Much more therefore should they be debarred in the New Law.
We shall speak of bigamy in the treatise on Matrimony (66).
I answer that, As appears from what we have said above (3,4,5), a man is disqualified from receiving Orders, either on account of an impediment to the act, or on account of an impediment affecting his personal comeliness. Hence he who suffers from a lack of members is debarred from receiving Orders, if the defect be such as to cause a notable blemish, whereby a man's comeliness is bedimmed (for instance if his nose be cut off) or the exercise of his Order imperilled; otherwise he is not debarred. This integrity, however, is necessary for the lawfulness and not for the validity of the sacrament.
This suffices for the Replies to the Objections.
Source: Summa Theologica (New Advent)