Pressure from environmental nongovernmental organizations and the public has accelerated research on the development of innovative and renewable polymers and additives. Recently, biobased “green” plasticizers that can be covalently attached to replace toxic and migratory phthalate-based plasticizers have gained a lot of attention from researchers. In this work, we prepared an azide-functionalized soybean oil derivative (AzSBO) and investigated whether it can be used as a plasticizer. We covalently attached AzSBO to an electron-deficient triple-bond-containing polyester via a metal-free azide–alkyne click reaction. The thermal, mechanical, and solvent absorption behaviors of different amounts of azidated oil-containing polyesters were determined. Moreover, the plasticization efficiency of AzSBO was compared with the commercial plasticizers bis(2-ethylhexyl) phthalate and epoxidized soybean oil. At relatively lower AzSBO ratios, the degree of cross-linking was higher and thus the plasticization was less pronounced but the solvent resistance was significantly improved. As the ratio of AzSBO was increased, the glass transition temperature of the pristine polymer decreased up to 31 °C from 57 °C. Furthermore, the incorporation of AzSBO also improved the thermal properties and 20% AzSBO addition led to a 60 °C increase in the maximum weight loss temperature.