We consider a relativistic vector boson oscillator in the 1 + 2-dimensional spacetime background induced by spinning cosmic string, which is a linear topological defect, and we analyze the effects of spin parameter (̟\varpi) and angular deficit parameter (α) of the background on the energy of the system. To acquire this, we solve the corresponding form of the vector boson equation. We perform an exact solution and obtain an energy spectrum which depends on the parameters ̟ and α. Furthermore, we show that our results agree well with the previously announced results when \varpi = 0 and α = 1. This fact provides us an opportunity to analyze the effects of spinning topological defect-generated spacetime background on the energy of the vector boson oscillator and we discuss several interesting features of the system under consideration.