Learn Spanish (Spain): Creo que no.

In English, we use "so" to stand in for a whole idea. In Spanish, you don't translate "so" directly here. Instead, the set phrase is Creo que no, which literally means "I believe that no." To say "I think so," you would use Creo que sí.

Why is creo used here instead of a form of pensar (to think)?

In English, we use "think" for both the mental process of thinking and for expressing an opinion. In Spanish, pensar is mostly for the mental process, while creer (to believe) is used to express an opinion or an assumption. Therefore, "I don't think so" is translated using creo.

Can I just say No creo instead of Creo que no?

Not usually as a standalone answer. If you just say No creo, it feels unfinished, as if you are saying "I don't believe..." without saying what. You need the que no to complete the thought. Alternatively, you could say No lo creo, which means "I don't believe it."