I was wondering how to say I think so in Japanese, do you have to say 'watashi wa kore ga omoimasu' or a different thing?
そう思うよ/そう思いますよ。 (sou omou yo / sou omoimasu yo.) - closer to "I think so.".
そうだね/そうですね。（sou da ne / sou desu ne.) - That's right.
そうなんだ。（sou nanda.) - That's right. (but with more emphasis).
In the conversation context it is explicit that you're the one saying so there's no need to use 私は、僕は、俺は at the beginning.