Concrete made with recycled concrete aggregate (RCA) has poor durability behavior compared to its counterpart normal concrete, especially when concreting in a chemically aggressive environment. Hence, this research work aims to improve the acid attack resistance of recycled aggregate concrete by incorporating rice husk ash (RHA) and hybridization of alkali-resistant glass fiber (Ar-GF) and steel fiber (SF). The RCA substitution was kept constant at 75%, while cement was partially substituted with RHA at dosages of 10, 15, and 20%. The hybridization of Ar-GF to SF was included in each of these ages in the respective proportions of 0.5%–0.5%, 0.25%–0.75%, and 0.75%–0.25%. The methodology adopted was by evaluating the compressive strength of the specimens at 28, 56, and 120 days of exposure to 4.0% of sulfuric acid attack to determine any loss in their strength and weight. Afterward, field emission scanning electron microscopy and Fourier transform infrared-ray characterization methods were performed to study the microstructure properties. The results revealed that the specimen made with a mix combination of RHA15% and hybridization of Ar-GF0.5% and SF0.5% (S1–4) exhibited better resistance to sulfuric acid attack than the ordinary concrete (control). Furthermore, the results of the microstructural analysis demonstrated that the S1–4 specimen had less micro- and macropores with more calcium silicate hydrate gel than the control specimen. Therefore, it is concluded that this mixture can be used when concreting in harsh chemical environments.