Take a furring strip, maybe 2" to 3"wide and 3/4" thick, drill pilot holes, and screw that to the vertical wall with the hardware cloth underneath.  You are making a sandwich with the hardware cloth between the two pieces of wood.  Bend the hardware cloth out at a 90 degree angle.  Since you are worried about rodents I'd bury it a couple of inches.  
Cover the edge of the hardware cloth so all sharp points are covered.  You are not going to snag skin or clothing afterwards.  If you put screws through a hole in the hardware cloth it isn't going anywhere.  Just clamping it down tight will secure it.  The pilot holes should keep the strip from splitting but if you put fender washers on the screws you can really clamp it down.  The pilot holes make it easy to start the screws.  
This is the way I attach hardware cloth, 2x4 welded wire, and chicken wire to a flat wooden surface.