"I don't think so."
Translation:Я думаю нет.
Actually, your translation is probably even better than the one given here. :) "Я думаю нет" is more like "I think, no". "Я так не думаю" also carries its sarcastic connotation just like English "I don't think so" does.
My wife who is a native Russian speaker agrees, Я так не думаю should be accepted, and is more natural. I've submitted a report.
But "I think not" and "I don't think so" mean the same thing. It would be a little different to say "I don't think like that" (= I don't think that way).
Is it a Russian phrase ? Nonsense !!! Absolute nonsense, folks ! "Я так не думаю" - is the correct answer. Even the sentence - "Я думаю: "Нет." - is not a correct version in Russian here.
"Я не думаю" , means more "I am not using my brain" (not thinking), or maybe mods thought about it as a part of a larger sentence (than it make sense) "Ya ne dumayu [o ee]"
That's what I thought when I first saw it in Russian and wrote it in English.
Although Russian allows for some freedom in word order, "Я не думаю так" doesn't sound very natural. "Я так не думаю" is almost idiomatic in feel. I'm not a native Russian speaker, but that's the only way I've ever heard it spoken.