If you aren't growing any really tall things, you can make sort of box using chicken wire and 1x1 boards. Cut the pieces like the pieces of your raised bed and nail them together. Staple the bottom of the chicken wire to the boards and cut a foot or two tall piece of 1x1 and nail one on each corner to hold the wire up. Tie a top layer of wire as wide and long as the box to the 4 posts and the other wire and it's a nice little removable barrier that most rodents won't be able to get through.
Vicki has a good point to remember that rabbits burrow. If the garden plants are growing up from the soil at ground level, then the garden enclosure will have to be sunken down below the surface so that rabbits simply do not go under it to get at the food.