The angular momentum of molecular cloud cores plays an essential role in the star formation process, because it is at the origin of the outflow and the jet, resulting in the formation of the protoplanetary disk, and defining the multiplicity of a stellar system. However, the time evolution of the angular momentum of molecular cloud cores is still unclear. In this study, we perform three-dimensional simulations using Godunov smoothed particle magnetohydrodynamics (GSPM) method to investigate the time evolution of the angular momentum of molecular cloud cores formed from magnetized filamentary molecular clouds. We run the simulations changing the strength of the initial magnetic field and study the effect of the magnetic field on the transfer of the angular momentum in the filamentary molecular clouds. As a result, we find that most of the cores rotate perpendicular to the filament axis in both weak and strong magnetic field cases. We also analyze the internal angular momentum structure of the cores. Although the cores gain angular momentum with various directions from the initial turbulent velocity fluctuations of their parent filaments, the angular momentum profile in each core converges to the self-similar solution in the region with the enclosed mass M<0.3Msun in the case of weak magnetic field. On the other hand, in the case of strong magnetic field, the magnetic braking is efficient and leads to a steeper slope of the internal angular momentum profile of the cores. In addition, we show that the rotation direction of inner region of the cores tend to be aligned with magnetic field direction in the case of strong mantic filed.