Is there such a thing as Turn based RP?

It could, but it has kinks in RPing fashion. I've done something similar in the Spam Zone.
http://www.kh-vids.net/showthread.php?113088-Dissidia-KHV-Final-Fantasy

I think the biggest thing would be deciding who goes first and whether they should post in a thread or PM you the move, as the latter could lead to less RPing fun and more waiting but the former can lead to unfairness

 

Unless I'm mistaken, there was talk of something similar to this a while ago, and it never really came into fruition.
I don't see why it wouldn't work, other than Final Fantasy's time-based 'turns', which would be difficult to pull off. A standard turn-based thing would be fine, though it would definitely require some level of dedication to the RP from its players, since posts would have to be made in a specific order.

 

As stated before, it can work. There's no real restriction with these kinds of things in the RP Arena. There has been interest shown towards these types of role plays. I've never seen a totally successful one, but with careful planning and dedication, along with some solid support, someone could pull it off. You'd just have to stick through with it.

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In technical terms, any battles that are waged in RPs should be turn based, to whatever extent possible (typically by way of people posting in rotations so they all get an equal opportunity to defend and counter against one another). Stat-based RPs have been made. I've seen them pretty often, though never to much success. Stats can only go so far in a text-based medium of role playing before it negates the creative writing aspects of the trade.

 

(Hah, necrobump) I'd just like to point out that I'm still interested in the long dead RP idea from long ago. Still willing to write the program and everything. Just Saiyan.