Objection 1. It would seem that the character of Order does not presuppose the character of Baptism. For the character of Order makes a man a dispenser of the sacraments; while the character of Baptism makes him a recipient of them. Now active power does not necessarily presuppose passive power, for it can be without it, as in God. Therefore the character of Order does not necessarily presuppose the character of Baptism.
Objection 2. Further, it may happen that a man is not baptized, and yet think with probability that he has been baptized. If therefore such a person present himself for Orders, he will not receive the character of Order, supposing the character of Order to presuppose the character of Baptism; and consequently whatever he does by way of consecration or absolution will be invalid, and the Church will be deceived therein, which is inadmissible.
On the contrary, Baptism is the door of the sacraments. Therefore since Order is a sacrament, it presupposes Baptism.
I answer that, No one can receive what he has not the power to receive. Now the character of Baptism gives a man the power to receive the other sacraments. Wherefore he that has not the baptismal character, can receive no other sacrament; and consequently the character of Order presupposes the character of Baptism.
Reply to Objection 1. In one who has active power of himself, the active does not presuppose the passive power; but in one who has active power from another, passive power, whereby he is enabled to receive the active power, is prerequisite to active power.
Reply to Objection 2. Such a man if he be ordained to the priesthood is not a priest, and he can neither consecrate, nor absolve in the tribunal of Penance. Wherefore according to the canons he must be baptized, and reordained (Extra De Presbyt. non Bapt., cap. Si quis; cap. Veniens). And even though he be raised to the episcopate, those whom he ordains receive not the Order. Yet it may piously be believed that as regards the ultimate effects of the sacraments, the High Priest will supply the defect, and that He would not allow this to be so hidden as to endanger the Church.
Source: Summa Theologica (New Advent)