Planar fractal microstructure is observed on the silver film treated by positive corona discharge for the first time. Due to the abundant positive ions driven by the electrical field of positive polarity, surface modification is mainly induced by the plasma oxidation effect, resulting in a large scale of dendritic pattern with self-similarity and hierarchy. In contrast, negative ions dominate the plasma-film interaction under negative corona discharge condition, leading to a different surface morphology without fractal characteristics. A growth model based on the modified diffusion-limited aggregation (DLA) theory is proposed to describe the formation of the dendritic fractal structure, whilst the physics behind is attributed to the electric field directed diffusion of the positive ions around the surface roughness. Numerical simulation verifies the high density of the hot spot in the dendritic pattern, which may enable potential applications in fractal photonic metamaterials.