My best suggestion would be to contact the FDACS Division of Plant Industry, located in Gainesville, FL. Someone there may know right offhand if it's considered toxic (at all). Otherwise, they probably know where to start looking to find the answer.
The final sentence under the Description section reads:
Although considered to be a species of yam, these plants are very toxic and should not be consumed.
(Emphasis theirs.) It doesn't mention tortoises per se, but it may encourage one to err on the side of caution.
The rhizome or bulb is hepatotoxic and perhaps renal toxic although same has been used medicinally in other cultures. No studies done on the leaves of which I am aware. Attached is one of the references on one of the toxicity studies on the rhizome. http://www.biosciencetrends.com/action/downloaddoc.php?docid=295
I was wondering this too. The woods near me are overgrown with these. Also, those ferns in the back look like Boston ferns which are safe for your tortoise. We have tons of those ferns in the woods too.