The cast iron plant (Aspidistra elatior) is not deer proof, but it is also not heavily browsed in the most deer-populated areas of San Antonio. However, this is really no indication of how much damage it might suffer in your area. You might test with a few plants before you commit to a larger planting.
Given that this is a rather small area and next to your house, fencing could discourage browsing. However, remember that hungry deer eat anything they can reach.