It stands for "has", but the full form is less likely because if you were writing formally (avoiding contractions) you would probably pay attention to the agreement.
Colloquially: "There's got to be some."
Somewhat more formally: "There have got to be some."
(Formally: "There have to be some.")
"There've got to be some" is less commonly seen and may even look a little odd to some people. "There has got to be some" would be open to criticism too, because "some things" is plural, so the agreement should be with "have".
Here "there's" is acceptable because it's clear that ordinary conversational English is in use. Indeed, it appears that you're writing a story or account in which this sentence is part of a direct quote (direct speech):
"There's got to be some."