No — and Here's Why
Paper towels, napkins and tissues are not accepted in curbside or drop-off recycling anywhere, for two reasons. First, their fibers are too short: paper towel pulp is usually made from paper that's already been recycled several times, and the fibers are too weak to be remade into new paper. Second, used towels are almost always soiled with food, grease or cleaning products, which contaminate a load of recyclables. Even clean, unused paper towels fail on the short-fiber problem.
Compost Them Instead (If Food-Soiled)
The better destination is compost — but only for the right ones. A paper towel or napkin used to wipe up food or water, or to dry your hands, is a carbon-rich "brown" and can go in a backyard compost bin or food-scrap drop-off. Do NOT compost paper towels that touched cleaning chemicals, disinfectants or grease and oil — those go in the trash. Unbleached brown towels compost best; heavily bleached white ones are better left out of home compost.
The Cardboard Tube Is Recyclable
One part of a paper towel roll is recyclable: the empty cardboard tube in the center. It's clean paperboard, so flatten it and put it in your cardboard/paper recycling (the same goes for toilet paper tubes). It's only the absorbent paper sheets themselves that can't be recycled.