Leviticus 14:29

And the rest of the oil that is in the priest’s hand he shall put upon the head of him that is to be cleansed, to make an atonement for him before the Lord.

Cross-reference

1 John 2:2 reveals Jesus as the propitiation for sins, fulfilling what the oil atonement here prefigured—the ultimate sacrifice behind the ritual.

Exodus 29:21 describes anointing Aaron and his sons with oil and blood for consecration, paralleling the application of oil here to set apart the cleansed leper.