  It is known that traversable wormhole can exist in General Relativity only if
its throat contains some exotic matter. In this paper, we obtain
$(2+1)$-dimensional (horizonless) charged magnetic brane without (curvature)
singularity. Then, we consider a nontrivial local transformation to grant a
global rotation to spacetime. After that, we generalize magnetic brane to
higher dimensional solutions and use the cut-and-paste method to construct
higher dimensional charged BTZ-like rotating wormholes such a way that they
reduce to charged magnetic BTZ solution in three dimensions, exactly. We also
show that charged BTZ-like wormhole supported by the exotic matter at its
throat $r=r_{+}$. Finally, we calculate the conserved quantities of the charged
BTZ-like wormhole such as mass, angular momentum and electric charge density,
and show that the electric charge depends on the rotation parameters,
interestingly, and the static wormhole does not have a net electric charge
density.
