In Genesis 28:22 Jacob makes a vow including a promise to give God a tenth (tithe) of whatever God gives to Jacob. Earlier we see Abraham give his tenth to the high priest of Salem, Melchizedek. And later, of course, a tithe is given to the Levites. But how was Jacob to give a tithe to God since there were no priests yet in his day?
Before we can determine just how Jacob would pay his tithes, we have to examine the entire context of the passage.(Gen. 28:17-22)
Jacob sets his head down in a particular place, upon a rock, and he discovers that God is in this place and angels are ascending and descending. He then declares,"
So the context is the House of God, which would become the physical Temple. It is to the Temple that the tithes are paid; and where the storehouse is kept.(Mal. 3:10)
Jacob's vow must be understood as more than an obligation: it is the promise of blessing that a Covenant God made with Abraham, confirmed through Isaac, and now he was the next in line to whom "All the families of the earth will be blessed".(Gen. 12:3)
The tithe is to be understood as part of our worship (Gen. 14:20),
Following Jacob's vow, he departed for Syria, where Laban, the brother of Rebecca his mother was. And after he came back, he was reminded by God of his vow(Gen 35:1), and he built an altar (Gen.35:3) :
The tithe is the physical action in our worship to God, in honor of His Blessing and Provision in our lives. It doesn't exist as a separate act, but it is part of our response to God. That is why the tithes were to be "brought to the storehouse"(Mal. 3:10), it is the place in the Temple where the tithes were kept and to be distributed.
Jacob's act of building an altar, and later, pouring out offerings and making sacrifices on that altar, are a precursor to the "tithes" he would pay through his children, and later, his children by faith-who "rest" upon the Rock that Jacob had lain his head.
Tithe is not limited to giving to the Levites and not only priests received tithe. Deuteronomy 14: 28 - 29 talks about the 'poor tithe'. It is more likely that Jacob started giving to the poor than looking for Melchizedek. After the destruction of the Temple, tithe went to the poor as it must have been in the time before the priesthood.