Most low molecular weight platinum-based anticancer drugs have a short circulation time in the bloodstream. One of the potential strategies to improve the targeted delivery of cisplatin and prolong its circulation is via the use of nanocarriers. An improved drug delivery system was developed via reversible addition-fragmentation chain transfer (RAFT) polymerization. In a one-pot reaction, the incorporation of anticancer drug and core cross-linking was simultaneously carried out by using the highly effective reaction of isocyanate groups in the core of the polymeric micelles poly(oligo(ethylene glycol) methyl ether methacrylate)-block-poly(styrene-co-3-isopropenyl-α,α-dimethylbenzyl isocyanate) (POEGMA-block-P(STY-co-TMI)) with amine groups in the prepared platinum(IV) drug. The micelles with platinum(IV) incorporated with a size of 36 nm were very stable in water. In a reductive environment, in this study simulated using ascorbate, the drug was released at a slow rate of 82% in 22 days and at the same time the cross-linked micelle broke down into free block copolymers as evidenced using inductively coupled plasma-mass spectrometer (ICP-MS), size exclusion chromatography (SEC), and dynamic light scattering (DLS). The in vitro study also revealed the promising antitumor activity of prepared platinum(IV) drugs encapsulated into the micelle structure.