I don't think so; while the leaves are very similar the stems on this look too thick and wiry to me. They are both in the same plant family so it *could* be sweet potato (also safe) but I don't think that's what it is.Sweet potato leaves.
I did a quick Google search for 'morning glory' and it's close but I don't think so. There's never any flowers that bloom out of it. Just a whole bunch of leaves from wiry stems.You eat this? It looks like morning glory, which I suppose *is* edible, even if not common in the U.S.
If that's what it is, the leaves are safe in moderation for testudo tortoises and my Russian likes it now and again. African tortoises I don't know.
If it's morning glory you'll also probably get several responses here saying it's dangerous. It's the seeds that are considered dangerous, not the leaves. The one concern I have with morning glory is that the stems are so thick and intertwined that I worry about my tortoise getting caught up in them; I pull the stems apart a bit and cut them up so that my very small tortoise isn't at any risk.
I think these just might be it because I'm seeing images of stir-fried dishes of them on Google images. Would there be any other plants that may be confused with or have similar leaves to these? The only other thing I know about the plant in question is that they require a lot of water according to my parents.Sweet potato leaves.