We demonstrate a field-effect nonvolatile memory device made of a ferroelectric copolymer gate nanodot and a single-walled carbon nanotube (SW-CNT). A position-controlled dip-pen nanolithography was performed to deposit a poly(vinylidene fluoride-ran-trifluoroethylene) (PVDF-TrFE) nanodot onto the SW-CNT channel with both a source and drain for field-effect transistor (FET) function. PVDF-TrFE was chosen as a gate dielectric nanodot in order to efficiently exploit its bipolar chemical nature. A piezoelectric force microscopy study confirmed the canonical ferroelectric responses of the PVDF-TrFE nanodot fabricated at the center of the SW-CNT channel. The two distinct ferroelectric polarization states with the stable current retention and fatigue-resistant characteristics make the present PVDF-TrFE-based FET suitable for nonvolatile memory applications.