Yes, but the more typical construction would be: I thought that you could do it. To say "I thought that you can do it" would be understood, but obvious that you are not a native speaker. The meaning would be clear, however. To be grammatically correct you should say "I thought that you could do it".

It should be "I think (that) you can do it." or "I thought (that) you could do it." You can put "that" in there or take it out, it means the same either way.