The motor, made from a single molecule just a billionth of a metre across, is reported in Nature Nanotechnology.
The minuscule motor could have applications in both nanotechnology and in medicine, where tiny amounts of energy can be put to efficient use.
Tiny rotors based on single molecules have been shown before, but this is the first that can be individually driven by an electric current.
"People have found before that they can make motors driven by light or by chemical reactions, but the issue there is that you're driving billions of them at a time - every single motor in your beaker," said Charles Sykes, a chemist at Tufts University in Massachusetts, US.
"The exciting thing about the electrical one is that we can excite and watch the motion of just one, and we can see how that thing's behaving in real time," he told BBC News.
The butyl methyl sulphide molecule was placed on a clean copper surface, where its single sulphur atom acted as a pivot.
The tip of a scanning tunnelling microscope - a tiny pyramid with a point just an atom or two across - was used to funnel electrical charge into the motor, as well as to take images of the molecule as it spun.
It spins in both directions, at a rate as high as 120 revolutions per second.
But averaged over time, there is a net rotation in one direction.
By modifying the molecule slightly, it could be used to generate microwave radiation or to couple into what are known as nano-electromechanical systems, Dr Sykes said.
"The next thing to do is to get the thing to do work that we can measure - to couple it to other molecules, lining them up next to one another so they're like miniature cog-wheels, and then watch the rotation propagation down the chain," he said.
As well as forming a part of the tiniest machines the world has ever seen, such minute mechanics could be useful in medicine - for example, in the controlled delivery of drugs to targeted locations.
But for the moment, Dr Sykes and his team are in contact with the Guinness Book of World Records to have their motor certified as the smallest ever.