  We define the notion of a holomorphic bundle on the noncommutative toric
orbifold $T_{\theta}/G$ associated with an action of a finite cyclic group $G$
on an irrational rotation algebra. We prove that the category of such
holomorphic bundles is abelian and its derived category is equivalent to the
derived category of modules over a finite-dimensional algebras $\Lambda$. As an
application we finish the computation of $K_0$-groups of the crossed product
algebras describing the above orbifolds initiated by Kumjian, Walters and Buck.
Also, we describe a torsion pair in the category of $\Lambda$-modules, such
that the tilting with respect to this torsion pair gives the category of
holomorphic bundles on $T_{\theta}/G$.
