Instances of synthetic polymers obtained from renewable feedstock with the possibility of post-synthesis functionalization are scarce. Herein, the first ever synthesis and drug delivery application of amphiphilic block copolymer (mPEG-b-PJL) derived from renewable jasmine lactone with free allyl groups on the backbone is presented. The polymer is synthesized via facile ring-opening polymerization and subsequently, UV mediated thiol-ene click chemistry is utilized for post-functionalization. The introduction of hydroxyl, carboxyl, and amine functionality to mPEG-b-PJL polymer is successfully established. As a proof-of-concept demonstration, doxorubicin (DOX) is conjugated on hydroxyl-terminated polymer (mPEG-b-PJL-OH) via redox responsive disulfide linkage to obtain PJL-DOX. PJL-DOX is readily self-assembled into micelles with an average hydrodynamic size of ≈150 nm and demonstrates reduction-responsive DOX release. Micelles are evaluated in vitro for cytocompatibility and selective drug release in cancer cells (MDA-MB-231) using 10 mm glutathione as a reducing agent. Cytotoxicity and microscopy results confirm a redox-triggered release of DOX, which is further confirmed by flow cytometry. The introduction of these novel functional polymers can pave the way forward in designing polymer-drug conjugate-based smart nano-carriers.