Synthetic biodegradable elastomers are an emerging class of materials that play a critical role in supporting innovations in bioabsorbable medical implants. This work describes the synthesis and characterization of poly (glycerol-co-sebacate)-cinnamate (PGS-CinA), a biodegradable elastomer based on hyperbranched polyesters derivatized with pendant cinnamate groups. PGS-CinA can be prepared via photodimerization in the absence of photoinitiator using monomers that are found in common foods. The resulting network exhibits a Young’s modulus of 50.5 to 152.1 kPa and a projected in vitro degradation half-life time between 90 and 140 days. PGS-CinA elastomers are intrinsically cell adherent and support rapid proliferation of fibroblasts. Spreading and proliferation of fibroblasts are loosely governed by the substrate stiffness within the range of Young’s moduli in PGS-CinA networks that were prepared. The thermo-mechanical properties, biodegradability, and intrinsic support of cell attachment and proliferation suggest that PGS-CinA networks abroadly applicable for use in next generation bioabsorable materials including temporary medical devices and scaffolds for soft tissue engineering.