You can pet a turtle. However, turtles do not generally enjoy being handled and petted in the same way other domestic animals do. Some turtles will be more fond of handling and petting than others. When petting and handling a turtle, you will need to ensure you do so safely and be sure not to stress out or harm them. Equally, you will need to ensure you wash your hands before and after to ensure you do not become ill from the salmonella bacteria they inherently carry.