We have developed and simulated a planar complementary Archimedes-based metamaterial absorber with the goal of its application in refractive index sensing. Unlike designs that employ multiple layers or numerous resonators within a single unit cell, our proposed absorber adopts a more streamlined approach. It consists of three layers, with an FR4 dielectric substrate sandwiched between two copper layers. It's important to note that the absorption characteristics of this design are polarization-dependent. This polarization dependence arises from the asymmetrical resonance behavior observed in both the x and y directions. The absorber exhibits impressive absorption rates at various resonance frequencies, namely 98.5% at f1 = 8.49 GHz, 77.1% at f2 = 8.88 GHz, 88.7% at f3 = 9.3 GHz, 98.2% at f4 = 9.87 GHz, 99.7% at f5 = 10.65 GHz, 83.4% at f6 = 11.58 GHz, and 99.9% at f7 = 12.24 GHz. Furthermore, we've explored the refractive index sensing capabilities of this structure by introducing a 1 mm analyte layer on top of the patch structure. Through refractive index sensing analysis, we've determined that this absorber-based sensor yields an impressive high-quality factor value of 84.5, underscoring its sensitivity and precision. To gain a deeper understanding of the physical mechanisms at play, we've conducted an analysis of surface current distribution plots. Additionally, we've investigated the behavior of the absorber under varying polarization and incident angle conditions, ranging from zero degrees to sixty degrees. This comprehensive characterization positions our absorber as a promising candidate for microwave sensing applications.