  We study the effect of internal space rotation on the gravitational
properties of infinite straight and stationary cosmic string. From the
approximate solution of Einsten equations for the spinning Q-lump string we
obtain long range gravitational accelleration resembling that of a rotating
massive cylindrical shell. We also compute the angular velocity of the inertial
frame dragging and the angle of light deflection by the Q-lump string. Matter
accretion on to spinning strings can play a role in galaxy formation when the
angular velocity times the string width is comparable to the speed of light.
