  Using the ansatz of Matos and N\'{u}\~{n}ez, the present article proposes an
algorithm for generating several classes, not all independent, of
asymptotically flat rotating wormhole solutions in the Brans-Dicke Theory. The
algorithm allows us to associate a real number}$n$ \textit{with} \textit{each
static and generated rotating solution. We shall also demonstrate how to match
a rotating wormhole to a flat spacetime at the matter boundaries. The vacuum
string extensions of the solutions are straightforward. The physical
interpretations of the solutions are deferred.
