They have different meanings. New Oxford American Dictionary suppose | səˈpoʊz | verb 1 [with clause] assume that something is the case on the basis of evidence or probability but without proof or certain knowledge: I suppose I got there about half past eleven. think | θɪŋk | verb (past and past participle thought | THôt | ) 1 [with clause] have a particular opinion, belief, or idea about someone or something: she thought that nothing would be the same again | (be thought) : it's thought he may have collapsed from shock | [with infinitive] : up to 300 people were thought to have died. • [no object] (think of) have a particular opinion of: she did not think highly of modern art | I think of him as a friend.

People would understand what you mean, but it sounds less natural. I'm not sure I've heard a native speaker say it that way. Interestingly, you can say "I don't suppose" as an indirect way to ask something. For example, if you're telling someone you're going to lunch, "I don't suppose you'd care to join me?" is a polite and slightly old-fashioned way of inviting them to go with you.