How can I hang a rug on my outside patio concrete wall. It's an outdoor rug and since it's so pretty I decided to hag it on my patio wall instead of lying it on the floor. It's 2'7''x4'11''.

Best bet is to use a hammer drill and tapcom screws with a galvanized washer.
If you don't have a hammer drill, or any drill, you'll have to use cut nails and drive them in with a hammer

The screw method listed above is the best bet. The nails would work, but can lead to cracking of the concrete and you don't want that.