Two mechanisms for generating rotation in a volcanic plume have been shown. As the plume shoots up at an astounding 200 to 600 meters a second--winds from the environment surrounding the volcano can come into the picture as a horizontal vortex tube that is tilted and stretched as it travels up. This mechanism is similar to what is seen in thunderstorms. Additionally, eddies and vortices from the volcanic environment itself can form creating a horizontal vortex ring. This is what causes the lumpy-looking profile of the plume.
Image Courtesy of the Zina Deretsky/NSF