Objection 1. It would seem that deacons can confer this sacrament. For, according to Dionysius (Eccl. Hier. v) "deacons have the power to cleanse." Now this sacrament was instituted precisely to cleanse from sickness of the mind and body. Therefore deacons also can confer it.
Objection 2. Further, Baptism is a more excellent sacrament than the one of which we are speaking. But deacons can baptize, as instanced by the Blessed Laurence. Therefore they can confer this sacrament also.
On the contrary, It is written (James 5:14): "Let him bring in the priests of the Church."
I answer that, A deacon has the power to cleanse but not to enlighten. Hence, since enlightenment is an effect of grace, no sacrament whereby grace is conferred can be given by a deacon in virtue of his office: and so he cannot confer this sacrament, since grace is bestowed therein.
Reply to Objection 1. This sacrament cleanses by enlightening through the bestowal of grace: wherefore a deacon is not competent to confer it.
Reply to Objection 2. This is not a necessary sacrament, as Baptism is. Hence its bestowal is not committed to all in cases of necessity, but only to those who are competent to do so in virtue of their office. Nor are deacons competent to baptize in virtue of their office.
Source: Summa Theologica (New Advent)