Not as far as I know ... except for Section 8 rentals as mentioned below. But, it is certainly common sense!
However, all tenants have a right to "quiet enjoyment" of the premises ... and who can enjoy a breezy summer evening with windows open to the refreshing air if flocks of various insects are streaming in? Not to mention the occasional mouse or bird. Or little kids climbing in and out of open windows for fun?
I believe it would be very hard to get a good tenant to agree to rent a home without window screens unless the rent is way below market.. And, maybe not even then. Most tenants regard window screens as standard equipment and very important!