Yes, you can. Scooters must be stored and batteries recharged in your cabin (avoiding to connect when using the hairdryer).  Keep in mind that the scooter minimizes the available space within your cabin.
Due to safety considerations, wheelchairs and scooters cannot be stored in the corridors. Your personal scooter should be able to fit in a standard cabin with a limited entry doorway (58 cm on MSC Divina and MSC Armonia, 68 cm on MSC Lirica, MSC Sinfonia and MSC Opera, 62 cm on the others). If your scooter is larger than the dimension reported for your chosen ship, you should book an H cabin or rent a smaller scooter. Segways and other similar vehicles cannot be operated on board. They shall be confiscated and can be taken off the ship to be used while in port.