Hi! In which direction does a Cat Claw vine climb? Left or right?

Are you talking about the direction of twining? I can’t find a direct reference, but many plants will un-twine and reset themselves if you have them going in the wrong direction. (I also find many warnings about the invasivness of this vine.)

It grows outwards in whatever direction it can to attach. We had it along a backyard wall and it took over whatever it could, very destructive if it’s allowed to touch down onto you patio and get between cracks or under pavers.

It is considered a very invasive plant. You may find it hides more than your iron fence. There are advisories out about not planting it and trying to eradicate it if you are unlucky to have it growing on your property.

The bad news here

If you are in the Unite States, check that it is not a prohibited species before you put it in. If it is prohibited and you put it in, your neighbors can charge you with removing, controlling it.

I live in the Northern hemisphere. I have only seen vines grow using Right hand rule. that means looking from the top, counter-clockwise is up.
That is not the best vine to plant. I hope you have Roundup ready.