  We develop Floer theory of Lagrangian torus fibers in compact symplectic
toric orbifolds. We first classify holomorphic orbi-discs with boundary on
Lagrangian torus fibers. We show that there exists a class of basic discs such
that we have one-to-one correspondences between a) smooth basic discs and
facets of the moment polytope, and b) between basic orbi-discs and twisted
sectors of the toric orbifold. We show that there is a smooth Lagrangian Floer
theory of these torus fibers, which has a bulk-deformation by fundamental
classes of twisted sectors of the toric orbifold. We show by several examples
that such bulk-deformation can be used to illustrate the very rigid Hamiltonian
geometry of orbifolds. We define its potential and bulk-deformed potential, and
develop the notion of leading order potential. We study leading term equations
analogous to the case of toric manifolds by Fukaya, Oh, Ohta and Ono.
