Learn English – What do you call the motor that fuels the movement of a robotic arm

I believe this is normally called a "servo", short for "servomechanism":

servomechanism (n): In control engineering a servomechanism, sometimes shortened to servo, is an automatic device that uses error-sensing negative feedback to correct the action of a mechanism.1 It usually includes a built-in encoder or other position feedback mechanism to ensure the output is achieving the desired effect.2

Note: We don't say a servo "fuels" the movement of a robot arm. The verb "fuel" (or "power") is used to describe the power source for engines which require some kind of external fuel. Instead we would say the servo "drives" the movement of a robot arm.

Servos can be fueled/powered by a variety of sources. Electric is probably most common, but other options are such things as hydraulic or steam power.

(Edit) moooeeeep also suggests "actuator", which seems equally valid:

actuator (n): An actuator is a component of a machine that is responsible for moving and controlling a mechanism or system, for example by opening a valve. In simple terms, it is a "mover".

If you're asking for the purpose of writing science fiction, then either is fine. I've seen both used. "Actuator" seems to be more commonly used when talking about a mechanism's design:

"Built into the inside of the suit was a weblike network of miniature actuators that made contact with my skin every few centimeters" - Ready Player One, Ernest Cline

and "servo" seems to be used when talking about a mechanism's movement:

"The robot's servos kicked in immediately, buzzing erratically ... attempting to lock onto the source of the noise" - Dome City Blues, Jeff Edwards