Flexoelectricity is an electromechanical coupling between strain gradients and dielectric polarization. Flexoelectricity is gaining more interest as a consequence of recent advances in the field of soft materials, where larger flexoelectric effects have been observed [mishra2025modeling]. A novel finite element approach for flexoelectric special Cosserat rods has been presented, enabling the study of flexoelectric structures under large deformations. Traditionally, a three-dimensional flexoelectric theory involves higher-order interpolation functions [codony2021modeling], which can be computationally expensive. The current approach utilizes $C^0$ Lagrange basis functions to capture the large deformation of the flexoelectric rod, thereby easing the computational cost and model the flexoelectric effects. The presented flexoelectric rod model is mechanically derived from that of Simo and Vu-Quoc [simo1986three] and lays a foundation for studying highly deformable flexoelectric structures. The developed finite element formulation was validated both analytically [codony2021modeling] and through existing experimental data [mizzi2022experimental], and the solutions obtained were found to be in close correlation. Various problems involving complex rotations of a flexoelectric rod can be analyzed using the proposed computational scheme. The developed flexoelectric systems have a wide range of applications, including sensors, energy harvesters, actuators, and biomedical devices.