  With an appropriate combination of three Liouville-type dilaton potentials,
we construct a new class of spinning magnetic dilaton string solutions which
produces a longitudinal magnetic field in the background of anti-de Sitter
spacetime. These solutions have no curvature singularity and no horizon, but
have a conic geometry. We find that the spinning string has a net electric
charge which is proportional to the rotation parameter. We present the suitable
counterterm which removes the divergences of the action in the presence of
dilaton potential. We also calculate the conserved quantities of the solutions
by using the counterterm method.
