A new acrylamide monomer, N-isopropyl-N-(3-(isopropylamino)-3-oxopropyl)acrylamide (M3i), consisting of both isopropyl and isopropylamidopropyl moieties, has been synthesized from isopropylamine and N-isopropylacrylamide via an aza-Michael addition reaction followed by amidation with acryloyl chloride. The homopolymer of M3i (polyM3i) and a series of random copolymers of M3i and poly(ethylene glycol)methyl ether acrylate (PEGA: CH2CHCO2(CH2CH2O)nMe, Mn = 480, n = 9 on average) with varying compositions have been synthesized via reversible addition-fragmentation chain transfer polymerization using 2-(dodecylthiocarbonothioylthio)-2-methylpropionic acid (DDMAT) as well as 1-phenylethyl phenyl dithioacetate (PEPD) as a RAFT agent. These polymers have been characterized by 1H NMR, FTIR, GPC, UV-Vis, fluorescence, TGDTA, DSC, DLS, and TEM techniques. A lower critical solution temperature (LCST) and glass transition temperature (Tg) for polyM3i prepared using DDMAT were observed at 17 and 133 °C, respectively, while for a polymer formed using PEPD, no LCST was observed until 0 °C and its observed Tg was found at 127.3 °C. The polymers are thermally stable up to 300 °C. Upon an increase in the M3i content in the copolymers, LCST decreases, Tg increases, and the apparent hydrodynamic diameter decreases. Moreover, the effects of concentration and the addition of urea and sodium chloride on the LCST of the copolymer with an LCST close to body temperature were studied. Owing to the incorporation of PEGA, a higher critical micellar concentration and larger TEM particle size of this copolymer were observed with respect to those of polyM3i. The usefulness of the micelles of the copolymers as nano-carriers for the drug doxorubicin was explored. The in vitro tumoricidal activity of the micelles of the doxorubicin-loaded copolymers was also assessed against Dalton's lymphoma cells.