  We consider charged rotating BTZ black holes in 2+1 dimensions and obtain 1+1
dimensional holographic superconductors on a spatial circle in the context of
the $AdS_3/CFT_2$ correspondence. The charged condensate for the boundary
superconductor is computed both in the analytic and the numerical framework in
a probe limit and a low angular momentum approximation. A critical value of the
angular momentum for the onset of superconductivity is established. We also
numerically compute the electrical conductivity of the 1+1 dimensional boundary
theory on a circle. The conductivity exhibits a dependence on angular momentum
of the rotating black hole both for the normal and the superconducting phase of
the boundary field theory. The significance of the boundary field theory in the
context of a Fermi-Luttinger liquid on a circle is discussed.
