Objection 1. It would seem that the state of slavery is not an impediment to receiving Orders. For corporal subjection is not incompatible with spiritual authority. But in a slave there is corporal subjection. Therefore he is not hindered from receiving the spiritual authority which is given in orders.
Objection 2. Further, that which is an occasion for humility should not be an impediment to the reception of a sacrament. Now such is slavery, for the Apostle counsels a man, if possible, rather to remain in slavery (1 Corinthians 7:21). Therefore it should not hinder him from being raised to Orders.
Objection 3. Further, it is more disgraceful for a cleric to become a slave than for a slave to be made a cleric. Yet a cleric may lawfully be sold as a slave; for a bishop of Nola, Paulinus, to wit, sold himself as a slave as related by Gregory (Dial. ii.). Much more therefore can a slave be made a cleric.
Objection 4.On the contrary, It would seem that it is an impediment to the validity of the sacrament. For a woman, on account of her subjection, cannot receive the sacrament of Orders. But greater still is the subjection in a slave; since woman was not given to man as his handmaid (for which reason she was not made from his feet). Therefore neither can a slave receive this sacrament.
Objection 5. Further, a man, from the fact that he receives an Order, is bound to minister in that Order. But he cannot at the same time serve his carnal master and exercise his spiritual ministry. Therefore it would seem that he cannot receive Orders, since the master must be indemnified.
I answer that, By receiving Orders a man pledges himself to the Divine offices. And since no man can give what is not his, a slave who has not the disposal of himself, cannot be raised to Orders. If, however, he be raised, he receives the Order, because freedom is not required for the validity of the sacrament, although it is requisite for its lawfulness, since it hinders not the power, but the act only. The same reason applies to all who are under an obligation to others, such as those who are in debt and like persons.
Reply to Objection 1. The reception of spiritual power involves also an obligation to certain bodily actions, and consequently it is hindered by bodily subjection.
Reply to Objection 2. A man may take an occasion for humility from many other things which do not prove a hindrance to the exercise of Orders.
Reply to Objection 3. The blessed Paulinus did this out of the abundance of his charity, being led by the spirit of God; as was proved by the result of his action, since by his becoming a slave, many of his flock were freed from slavery. Hence we must not draw a conclusion from this particular instance, since "where the spirit of the Lord is, there is liberty" (2 Corinthians 3:17).
Reply to Objection 4. The sacramental signs signify by reason of their natural likeness. Now a woman is a subject by her nature, whereas a slave is not. Hence the comparison fails.
Reply to Objection 5. If he be ordained, his master knowing and not dissenting, by this very fact he becomes a freedman. But if his master be in ignorance, the bishop and he who presented him are bound to pay the master double the slave's value, if they knew him to be a slave. Otherwise if the slave has possessions of his own, he is bound to buy his freedom, else he would have to return to the bondage of his master, notwithstanding the impossibility of his exercising his Order.
Source: Summa Theologica (New Advent)