In the fight against antibiotic resistance, which is rising to dangerously high levels worldwide, new strategies based on antibiotic-conjugated biocompatible polymers bound to magnetic nanoparticles that allow the drug to be manipulated and delivered to a specific target are being proposed. Here, we report the direct surface engineering of nontoxic iron oxide nanoparticles (IONs) using biocompatible dextran (Dex) covalently linked to β-cyclodextrin (β-CD) with the ability to form non-covalent complexes with silver-sulfamethazine (SMT-Ag). To achieve a good interaction of β-CD-modified dextran with the surface of the nanoparticles, it was functionalized with diphosphonic acid (DPA) that provides strong binding to Fe atoms. The synthesized polymers and nanoparticles were characterized by various methods, such as nuclear magnetic resonance (NMR), Fourier transform infrared (FTIR) and ultraviolet–visible (UV–Vis) spectroscopies, transmission electron microscopy (TEM), thermogravimetric analysis (TGA), atomic absorption spectroscopy (AAS), dynamic light scattering (DLS), etc. The resulting magnetic ION@DPA-Dex-β-CD-SMT-Ag nanoparticles were colloidally stable in water and contained 24 μg of antibiotic per mg of the particles. When tested for in vitro antimicrobial activity on Gram-positive (Staphylococcus aureus) and Gram-negative (Escherichia coli) bacteria and fungi (yeast Candida albicans and mold Aspergillus niger), the particles showed promising potential.