  We propose a codimension two warped braneworld model within the teleparallel
$f(T)$ gravity. By assuming a global vortex as the source, we found a $l=0$
vortex solution that yields to a thick string-like brane. Asymptotically, the
bulk geometry converges to an $AdS_6$ spacetime whose cosmological constant is
produced by the torsion parameters. Furthermore, the torsion induces an
$AdS-dS$ transition on the exterior region. Inside the brane core, the torsion
produces an internal structure even for a single complex scalar field. As the
torsion parameters vary, the brane undergoes a phase transition leading to the
formation of ring-like structures. The bulk-brane Planck mass ration is
modified by the torsion. The analysis of the stress energy condition reveals a
splitting brane process satisfying the weak and strong energy conditions for
some values of the parameters. In addition, we investigate the behaviour of the
gravitational perturbations in this scenario. It turns out that the
gravitational spectrum has a linear behaviour for small masses and is
independent of the torsion parameters for large masses. In the bulk, the
torsion keeps a gapless non-localizable and stable tower of massive modes.
Inside the brane core the torsion produces new barriers and potential wells
leading to small amplitude massive modes and a massless mode localized around
the ring structures.
