image from piajanebijkerk.com
Is this as appealing to you as it is to me? Certainly this could be artistically created with some driftwood or other branches woven or wired together, but I think it would be great to grow this naturally. Here is a list of ideas and plants that I think you can use to create a natural arbor. If you think of something else that could work too, feel free to add to the list in the comments.
1) Wisteria (with a good frame for support. – I think a large curved metal arc would hold the heavy vine, but ultimately disappear inside the woody stems.
2) Grapes (again with the frame)
3) Bittersweet (NOT Planted! – but after you cut this invasive weed out of a nearby forest) Bittersweet can have very interesting curling woody branches that can be used to create sculptures (see this video of weed warriors who create art from bittersweet vine)
4) Mountain Laurel or Rhododendron (Pruned and Trained – and lots of patience for these slow growers)
5) Eucalyptus or other downed wood (like this sculpture below by Pavel Perina) Make it more interesting with Curly willow or Curly hazel.