  We study the rotor-router walk with the clockwise ordering of outgoing edges
on the semi-infinite cylinder. Imposing uniform conditions on the boundary of
the cylinder, we consider growth of the cluster of visited sites and its
internal structure. The average width of the surface region of the cluster
evolves with time to the stationary value by a scaling law whose parameters are
close to the standard KPZ exponents. We introduce characteristic labels
corresponding to closed clockwise contours formed by rotors and show that the
sequence of labels has in average an ordered helix structure.
