The effect, reported in Science, is similar to the action of muscles found in elephant trunks and squid tentacles.
However, the yarns twist 1,000 times as much as previous "artificial muscles".
The effect, which occurs thanks to a conducting fluid in which the yarns were dipped, could be put to use in motors much thinner than a human hair.
The team of researchers from Australia, the US, Canada and South Korea demonstrated motors that could spin at nearly 600 revolutions per minute, turning a weight 2,000 times heavier than the yarn itself.
Carbon nanotubes have only recently been identified by scientists; they are "straws" made only of atoms of carbon linked together in hexagons. They have remarkable physical properties - being more than 100 times stronger than steel.
Ray Baughman of the University of Texas at Dallas is a renowned researcher into the tubes' properties, and is a co-author of the new research.
"The carbon nanotube yarns comprise individual nanotubes - untold billions of them - that are about 1/100,000th the diameter of a human hair," he told the podcast of Science magazine.
The yarns were made by pulling sheets of nanotubes from "forests" of the tubes and twisting them to form a coiled structure - much as yarn is made from wool.
They were then dipped in an electrolyte - a fluid containing ions, electrically charged atoms. When a voltage was applied at the ends of the yarns, these ions moved into the fibres, causing them to expand.
Because of their coiled shape, this expansion led to them "doing the twist".
"The torque that we can generate per mass of the yarn is comparable to that of very large electric motors," said Prof Baughman.
"But as you down-size electric motors you dramatically decrease... the torque capabilities per weight, and make the motors very expensive."
He said that motors made from the yarns would find use in what is known as microfluidics, "for chemical 'labs on a chip' that can be used for analysis of chemicals, or for sensing".
"Often you want to control the movement of fluids, you want to pump them from one place to another or turn off one flow and open up another, and the carbon nanotube muscles because of their very small size seem very suitable for this type of application."
Yarns made of the tiny straws of carbon called nanotubes have an astounding ability to twist as they contract, scientists have found.