Both are correct, but "have" would be the more common and logical choice.
The decision whether to think of "two thirds" as singular or plural is not a mathematical one. The decision depends on how YOU think of "two thirds". Do you think of it (in this instance) as a singular, or do you think of it as a plural? You can think of it sometimes one way and sometimes the other. Anabelle's answer is correct FOR HER because she thinks of "two thirds" as a plural. If you choose to view "two thirds" the same way that she does, then you also should regard "two thirds" as plural.
However, that is not the only "correct" choice. Your brain has the liberty to override the common logic and think of plural things as singular, if it wants to do so. For example, you are free to say "A thousand people is too many for this room to hold at one time." Here's another example: "Jack, Mary, and Bob together is such a sight to behold".
You are in charge, not mathematics.