Three poly(ethylene glycol)–poly(ε-carprolactone) (PEG–PCL) copolymers with different topologies but identical molar ratio between PEG to PCL were designed. These copolymers, namely, diblock (L-PEG–PCL), triblock (B-PEG–PCL), and star shaped (S-PEG–PCL) copolymers, were extensively characterized by ¹H Nuclear Magnetic Resonance (¹H NMR), Fourier Transform Infrared Spectroscopy (FTIR), and Gel Permeation Chromatography (GPC) analyses. The effect of topology on crystallization was investigated by X-Ray Diffraction (XRD), Differential Scanning Calorimetry (DSC). Results showed that the diblock copolymer possessed the highest crystallinity, followed by triblock and star shaped copolymers. Although the topology did not affect the self-assembly behavior of copolymers, the effects on size, size distribution, drug loading content, and drug release rate of the polymeric micelles were observed. The micelles self-assembled from linear diblock copolymer achieved higher cellular uptake and lower half maximal inhibitory concentration (IC₅₀). These findings are favorable to establish the foundation to further design proper structure of amphiphilic copolymers as nanocarrier systems for efficient anticancer therapy.