We report on a theoretical study of collective electronic excitations in single-layer antimony crystals (antimonene), a novel two-dimensional semiconductor with strong spin-orbit coupling. Based on a tight-binding model, we consider electron-doped antimonene and demonstrate that the combination of spin-orbit effects with external bias gives rise to peculiar plasmon excitations in the mid-infrared spectral range. These excitations are characterized by low losses and negative dispersion at frequencies effectively tunable by doping and bias voltage. The observed behavior is attributed to the spin-splitting of the conduction band, which induces interband resonances, affecting the collective excitations. Our findings open up the possibility to develop plasmonic and optoelectronic devices with high tunability, operating in a technologically relevant spectral range.