In the Old Testament, the ‘anointing’ is usually the action of the pouring out of oil upon the recipient, whether a priest or king, but this process is nowhere mentioned for a prophet. The only mention of an anointing for a prophet is as an instruction to the prophet Elijah as recorded in 1 Kings 19:15b-16 (HCSB), “The Lord instructed Elijah, to go to Elisha son of Shaphat from Abel-meholah and anoint him as prophet in your place”. Elijah anointed Elisha by throwing his mantle over him (1 Kings 19:19). There is no mention of pouring oil on Elisha. There were many prophets throughout the Old Testament, individuals as well as companies of prophets (1 Samuel 19:20, NASB), or sons of prophets (2 Kings 4:1 HCSB), on which the Holy Spirit came and they prophesied for a particular occasion. But until the prophet received revelation, by means of the Holy Spirit, the prophet had nothing to communicate. Prophets were recognised by the people by the accuracy of their prophecies, not the outward sign of ‘anointing’.
In the New Testament, after Pentecost, we are all imbued with the Holy Spirit and therefore according to 1 Corinthians 12:10 can have the gift of prophecy, but not all are prophets as stated in 1 Corinthians 12:29. 1 Corinthians 12:28-30 and Ephesians 4:10-16 speak of offices or positions of authority to lead, guide and maintain the body, either locally, regionally or globally; often known as the 5-fold ministry. Those recognised by others as being appointed by the Spirit to the office of Prophet, ‘for the equipping of the saints for the work of service, to the building up of the body of Christ, until we each come into total agreement in the faith and knowledge Jesus has, that we are as perfect as the fullness of Christ within the Godhead’ (paraphrased Ephesians 4:12-13), may then be anointed with oil by their team leader (apostle or elder) before the congregation, so that they themselves and the congregation can recognize their appointment to the office.