When did Christ institute such a Sacrament?

The Catholic Answers

That is not known. But the fact that He did so is evident from the words of St. James. “Is any man sick among you? Let him bring in the priests of the Church, and let them pray over him, anointing him with oil in the name of the Lord. And the prayer of faith shall save the sick man: and the Lord shall raise him up: and if he be in sins, they shall be forgiven him.” James V., 14-15. When St. James says that he must be anointed in the name of the Lord, that he shall be saved, and that the Lord will raise him up, he shows most clearly that Christ Himself was the author of the commission to administer this sacramental rite.

Radio Replies Volume 1 by Rev. Dr. Leslie Rumble MSC and Rev. Charles Mortimer Carty