Magnetorheological fluids (MRFs) have been successfully used in a variety of smart control systems, but are still limited due to their relatively poor settling stability. Herein, a core/shell-structured Fe3O4/copolymer composite nanoparticle is synthesized as a new candidate material for stimulus-responsive MRFs to tackle the limitation of the long-term dispersion stability. Aniline-co-diphenylamine copolymers (PANI-co-PDPA) are loaded onto the surface of Fe3O4 nanoparticles, providing a lighter density and sufficient active interface for the dispersion of magnetic particles in the carrier medium. The features of the Fe3O4/copolymer composite nanoparticles, including morphology, compositional, and crystalline properties, are characterized. An MRF is prepared by suspending Fe3O4/copolymer composite nanoparticles in a nonmagnetic medium oil, and its rheological properties are assessed using a controlled shear rate test and dynamic oscillation tests using a rotational rheometer. Rheological models including the Bingham model and the Herschel–Bulkley model are fitted to the flow curves of the MRF. The obtained Fe3O4/copolymer composite shows soft-magnetic properties, as well as greater density adaptability and higher stability, compared to Fe3O4. Moreover, the sedimentation testing provides information about the dispersion stability characteristics of MRF and shows a good correlation with high-stability magnetorheological (MR) response. The Fe3O4/copolymer-based MRF with a tunable and instantaneous MR response is considered a promising material for smart control applications.