Cardiac activation mapping is critical for guiding catheter ablation of arrhythmias but remains challenging due to the difficulty of reconstructing wavefront propagation from sparse intracardiac catheter scans. Existing methods often neglect the physical laws governing electrical signal propagation in cardiac tissues. Approaches that do incorporate physics rely on isotropic models, assuming constant conduction velocity in all directions, and thus fail to account for the influence of fiber orientation, leading to physiologically inconsistent activation maps. In contrast to previous physics-informed frameworks that assume isotropic conduction, this article introduces a Physics-Informed Neural Network (PINN) framework that integrates the anisotropic Eikonal equation to embed the underlying physics of cardiac conduction and explicitly model the effect of myocardial fiber orientation on wavefront propagation, enabling physio-logically consistent reconstruction of cardiac activation maps that reflect these directional effects. The framework employs a dual-network architecture: one network estimates activation time φ(x), and the other reconstructs the direction-dependent conduction velocity tensor D(x) from sparse intracardiac catheter data.Evaluated on a dataset with sharp conductivity transitions, the framework accurately reconstructed activation times (NRMSE:1.67%) and captured key features of conduction anisotropy. This physics-consistent approach represents a significant step toward clinically reliable cardiac activation maps for ablation planning.