Yes you can clean your car windows and even your windshield using paper towels.
Regular paper towels will work fine to clean your car windows and windshield although shop paper towels or shop towels are better.
But I've had no issue cleaning my cars windows and my cars windshield using paper towels.
I spray some Windex onto the window and windshield and then use the paper towel in a circle motion to clean the cars windows and windshield.
I've never had any issues or streaks etc with regular paper towels.
Also the old style cloth diapers work well as a cleaning rag for windows including house windows, car windows, windshields etc.
They are lint free and work well as cleaning rags.