Fractal and optical characteristics of self-affine surfaces of silver(Ag) thin films deposited through direct current (dc) magnetron sputtering as a function of thickness are investigated and explored here. The surface morphology of Ag thin films is characterized by field emission electron microscopy, and atomic force microscopy technique. The cube counting algorithm is used to extract the fractal dimension of Ag thin film. The surface roughness (interface width) shows monotonic increases with film thickness, while the other parameters, such as lateral correlation length, roughness exponent, and fractal dimension exhibit linear variation with thickness. Our findings reveal distinctive scaling behaviors, with scaling exponents α, β, and 1/z indicating unique growth characteristics. The interface width w increases as a power law of thickness t, w(t)∝tβ, with β=0.39± 0.007, and the lateral correlation length ξ grows as ξt∝t1/z with 1/z=0.14± 0.002. The roughness exponent extracted from height-height correlation analysis is α=0.61–0.41. The self-affine nature of the Ag thin films is further confirmed by the autocorrelation function. X-ray photoelectron spectroscopy (XPS) is used to the confirm the growth of Ag thin film. Additionally, we have studied the role of fractal dimensions and lateral correlation length (ξ) on the surface plasmon resonance (SPR) of Ag thin film. Our results indicate a red-shifting behavior of SPR with increasing interface width (w), lateral correlation length (ξ), and fractal dimensions. This study suggests the significance of not only the roughness exponent and fractal dimension but also the local surface slope in SPR activity in Ag thin films.