Rat Proofing A Bedroom?

I have four rats and I allow them to run around my room during free time. I've rat proofed my bedroom, for the most part (picking up wires, making sure there is nothing dangerous they can eat, etc.). There's one thing I don't know how to fix. My bedroom and closet door have a large space under them (about an inch to two inches). At the moment I taped on a piece of the large cardboard papers onto the bottom of my bedroom door to keep them from getting out, but it wouldn't hold if they wanted to. I also tuck a sheet under my closet door to keep them from getting in there. We rent this place, so I can screw or nail anything on to the door, but I want to have something that permanent that I don't have to keep taking on and off when they come out. Any ideas? Thanks!