The Lord God, who gathers the outcasts

“And the foreigners who join themselves to the Lord, to minister to him, to love the name of the Lord, and to be his servants, everyone who keeps the Sabbath and does not profane it, and holds fast my covenant — these I will bring to my holy mountain, and make them joyful in my house of prayer; their burnt offerings and their sacrifices will be accepted on my altar; for my house shall be called a house of prayer for all peoples.”
The Lord God, who gathers the outcasts of Israel, declares, “I will gather yet others to him besides those already gathered.”
Isaiah 56:6-8


A promise

And it shall come to pass, if [the gentiles] will diligently learn the ways of my people, to swear by my name, ‘As YHVH lives,’ even as they taught my people to swear by Baal, then I will give them a place among my people.
Jeremiah 12:16

So far, this is the strongest promise to the gentiles that I know of. Most of the others are to Israel. But if the gentiles become part of YHVH’s people, the same promises apply to them.