  We obtain geodesically complete spacetimes generated by static and rotating
magnetic point sources in an Einstein-Maxwell-Dilaton theory of the Brans-Dicke
type in three dimensions (3D). The theory is specified by three fields, the
dilaton, the graviton and the electromagnetic field, and two parameters, the
cosmological constant and the Brans-Dicke parameter, w. When the Brans-Dicke
parameter is infinity, our solution reduces to the magnetic counterpart of the
BTZ solution, while the w=0 case is equivalent to 4D general relativity with
one Killing vector. The source for the magnetic field can be interpreted as
composed by a system of two symmetric and superposed electric charges. One of
the electric charges is at rest and the other is spinning.
