It will depend upon your state's laws however in many states you have to be at least 16 years of age to own a motorized scooter.
For example the California DMV quotes CA Vehicle Code 15500 which states that it is unlawful for any minor who does not possess a valid driver's license issued under this code to order, purchase or lease, attempt to purchase or lease, contract to purchase or lease, accept, or otherwise obtain, any vehicle of a type subject to registration.
In CA a motorized scooter is defined as a two-wheeled device that has handlebars, a floorboard designed to be stood upon when riding, and is powered by a motor. The California Vehicle Code does not require registration, license plates to be displayed or the scooter to be insured. Even though insurance is not required, owners of these scooters should contact their insurance company to determine if coverage is available.
Also in California an operator of a motorized scooter must be at least 16 years old, possess a valid driver's license or instruction permit, and wear a helmet. So here you need to be at least 16 years of age with a driver's license to own a motorized scooter.
In Maryland laws also state to get a moped or motor scooter license (and own such a vehicle) one must by 16 years of age or older. In MD a moped is defined as a bicycle that is designed to be operated by human power with the assistance of a motor, is equipped with pedals that mechanically drive the rear wheel, has 2 or 3 wheels (one of which is more than 14 inches in diameter) and has a motor with a rating of 1.5 brake horsepower or less. If the motor is an internal combustion engine then the capacity must be 50 cubic centimeters (cc) or less.
A motor scooter in MD is defined as a non-pedal vehicle that has a sear for the operator, 2 wheels (one of which is 10 inches or less in diameter), has a step-through chassis, has a motor with a rating or 2.7 brake horsepower or less or if an internal combustion engine it must have a capacity of 50 ccs or less and finally the scooter must be equipped with an automatic transmission.
To find out about your state's specific laws regarding the minimum age one can own a motor scooter check with your local Department of Motor Vehicles (DMV). If you are a minor you may also need to find out if to own one you must have a parent or guardian's name on the title and registration (if required by your state) with you. Some states require this of minors until they turn 18 and are considered by law an adult.