Looking for a vine for dry shade

Poison ivy?

Kidding.

Does Virginia creeper grow there? I think that does well in dry shade.

Great question.  Here are a couple that I have used in dry shade around oaks:

Ficus pumila (Creeping Fig)

Creeping Fig does well in sun or part shade and takes little irrigation (depending on where you live).  It can cling to walls and does not need any support.  Though, you should keep it pruned back.  I have seen it become top heavy and pull off of large parking structure.  If you want to play off of the oak leaf, there is a variety quercifolia.

Hardenbergia violacea (Lilac Vine)

This is an Australian native that does well in dryish shade.  It seems to bloom all the time, but it needs a support structure to grow.  If the wall has not been built yet, perhaps something like greenscreen would work for your application?

You could also try Parthenocissus tricuspidata (Boston Ivy) and Lonicera japonica (Honeysuckle).  Both do well in SoCal I believe.

I hope this helps!

Ficus pumila. Certainly does well on east-facing walls and I’ve seen it on north-facing wall too in USDA zone 9. This evergreen has attractive juvenile leaves which belie its eventual aggresiveness

I don’t know if this is available/suitable to your area :

Trachelospermum asiaticum

Jasmine smell, grows in shade, use as groundcover or climber. Trim if you’re not after ‘natural’ look