The straightforward translation will be: "отметить звёздочкой" to indicate "starring" action. This is 100% understandable but nevertheless sounds quite unnatural to native. Moreover there's no such straightforward equivalent for the opposite action - phrase "разометить звёзочкой" is incorrect.
Saying "добавить звёздочку" / "убрать звёздочку" (to add/to remove a star) is acceptable, but there's a subtle inconsistency between the action itself and the actions' description. Adding a star to some entity and starring it are a slightly different things.
But, yet there is no exact (especially "not slang") equivalent of "star"/"unstar" pair, words "залайкать"/"отлайкать" are very common in modern Russian web slang. Since those terms are very close in almost all cases, I'd recommend nervertheless this translation. I hardly believe you'll find anything more relevant.