Not safely, according to http://sneakykitchen.com/Ten_commandments/microwave_safety.htm
“All paper products are manufactured with chemicals. Never use grocery bags, paper plates, newspapers, butcher’s wrap or other paper items to heat food. The microwave can cause chemicals in these products to transfer into your food. Use white paper towels only if the label states they are microwave safe. Wax paper, parchment paper and oven cooking bags are safe to use. Don’t overheat!”
However, according to the USDA most paper plates should actually be safe to use http://www.fsis.usda.gov/FactSheets/Microwave_Ovens_and_Food_Safety/index.asp#11
“What containers and wraps are safe to use in the microwave oven?
Only use cookware that is specially manufactured for use in the microwave oven. Glass, ceramic containers, and all plastics that are safe to use usually will be labeled for microwave oven use.
“SAFE TO USE:
- Any utensil labeled for microwave use.
- Heatproof glass (such as Pyrex, Anchor Hocking, etc.).
- Glass-ceramic (such as Corning Ware).
- Oven cooking bags.
- Baskets (straw and wood) for quick warm-ups of rolls or bread. Line the basket with napkins to absorb moisture from food.
- Most paper plates, towels, napkins and bags. For optimal safety use white, unprinted materials.
- Wax paper, parchment paper, heavy plastic wrap. Do not allow plastic wrap to touch food; vent it to allow a steam escape.
- Heat-susceptor packaging. “