Anointed, as it was used in this verse,
is from the Greek word, chrio, meaning, To smear or rub with oil. Thoughout the history of Israel, special people entering into the service
of the Lord (such as priests and kings), were first anointed with oil, a Biblical symbol of the Holy Spirit.
These people received a measure of power from the Lord from this anointing.
But Jesus was anointed, not by a priest, but by God, and not with oil, but with the "Holy Ghost, and with power".

...God anointed Jesus of Nazareth with the Holy Ghost and with power: who went about doing good and healing all that were oppressed of the devil; for God was with Him. Acts 10:38