Gravitational field of a spinning sigma-model cosmic string

We study the effect of internal space rotation on the gravitational properties of infinite straight and stationary cosmic strings. From the approximate solution of Einstein equations for the spinning Q-lump string, we obtain long-range gravitational acceleration 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 onto spinning strings can play a role in galaxy formation when the angular velocity times the string width is comparable to the speed of light.