This work presents a novel Virtual Element (VE) formulation for the analysis of two-dimensional beam structures undergoing large displacements and finite rotations. The proposed approach builds upon the geometrically exact theory of initially curved beams originally introduced by Reissner in [1]. This theoretical framework provides a consistent description of finite rotations, shear deformation effects, and initial curvature, making it suitable for both slender and moderately thick beams. The proposed VE formulation extends the framework originally developed for two-dimensional Timoshenko beams by Wriggers in [2]. The element construction relies on suitable projection operators defined onto polynomial spaces and employs displacements and rotations at the element endpoints as the sole degrees of freedom. This feature is maintained even when higher-order approximation spaces are employed: additional unknowns arise only as internal variables not associated with any physical node and can therefore be efficiently condensed out at the element level. As a result, the formulation leads to a compact and computationally efficient element representation that can be readily integrated into standard finite element software environments. Some numerical examples are presented to assess the accuracy, convergence behavior, and robustness of the proposed formulation. Benchmark problems involving arbitrary initially curved beam configurations subjected to large deflections and rotations are considered. The results highlight the effectiveness of the VE approach for 2D geometrically exact non-linear initially curved beams. Moreover, numerical evidence indicates that the adoption of a curved beam formulation allows the recovery of the optimal convergence rates, in contrast to the suboptimal behavior observed when straight-axis beam models are applied to initially curved structures [3]. The proposed formulation contributes to recent advances in large-deformation beam modeling and represents a promising tool for innovative applications in geometrically non-linear structural analysis.