I have a covered run that is 4 ft tall, one that is angled with 6 ft at the peak and 4 ft at the edges, and finally two 6 ft tall one's. I MUCH prefer the 6 ft tall one's, it is easier to get in there with your birds, have access if there is a problem, and easier cleaning. You don't have to bend down all the time.
If you are planning on covering the run then 3 ft tall could work if you don't mind bending down all the time. I have seen some pictures on here where people have a short run but have access doors on top for easy access. They of course aren't very big. My runs range from 8ft x 8ft to 20ft x 30ft.
If you are not planning on covering it then I would say for sure it isn't tall enough. It would be easy access for a dog, coon, or any other predator to get to your birds. Of course the birds may also be able to escape.