Is it correct to say so? Does this mean the same as "thanks a lot"?
The commonly used expression, in AmE, is thanks a million. I think thanks a ton has derived from the same expression and eventually found its way to the mainstream. I can't find anything for thanks a ton in NOAD, but see an entry for thanks a million. Furthermore, I can't find the same expression registered in OED, which makes it chiefly American.
In American English, thanks a ton is atypical in written form. I have heard it spoken, not too often though. As others said, thanks a lot, or thanks a million, or thanks a bunch or even thanks much would be spoken and understood more often. Any of those would be informal but not slang usage in written American English.
Ton is not a metric unit, but rather, an English (Imperial?) system unit of the sort we use here in the U.S.A. as mentioned by @Urbycoz in a comment. Despite that, thanks a ton is less common than other expressions, even in American English. You will probably be understood though.
Given that the intent is to express gratitude, it is especially important to be easily understood! I would use an expression where there isn't any chance of misinterpretation.