You are absolutely not allowed to sit on or touch a giant tortoise. Not only is sitting on a giant tortoise illegal in the Galapagos, but it is also extremely stressful for the tortoises. While their shells are very strong, tortoises are sensitive to touch through their shells.
As per the Galapagos National Park rules, you must remain at least 6ft (2m) from the Galapagos tortoises.