There is no single scripture which they use. There's a bunch all put together.
1st: 1 Corinthians 11:27 "So then, whoever eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of sinning against the body and blood of the Lord."
This scripture shows that SOME people are not worthy to partake. So there must be some kind of qualifications.
2nd: Luke 22:20 Jesus says: This cup is the new covenant in my blood, which is poured out for you.
So the people who are part of the new covenant should partake.
3rd: Luke 22:29 "And I confer on you a kingdom, just as my Father conferred one on me"
They say THIS is the new covenant. That they rule in the 'kingdom'
4th: Daniel 2:44 "God of heaven will set up a kingdom that will never be destroyed, nor will it be left to another people."
They believe that this is the 'kingdom' Jesus was talking about.
5th: Revelation 5:10 "You have made them to be a kingdom and priests to serve our God, and they will reign over the earth"
So they think this meens that the ones in the new covenant are eventually gonna reign over the earth in the kingdom.
6th: Revelation 7:9, 14 In short this says that 144,000 are gonna be ruling in the kindom in heaven over a great multitude that came out of the tribulation.
So if you put it all together it means that only the ones who are gonna rule in heaven as part of the 144,000 are part of the new covenant and therefore qualified or 'worthy' to partake.