Ferroelectric capacitive memory (FeCAP) holds enormous potential for low-power, high-density in-memory computing. While hafnia-based FeCAPs have attracted attention for their silicon compatibility, they suffer from limited performance, such as a narrow memory window and relatively high switching fields. In this work, an FeCAP device is developed on the basis of a single-crystalline barium titanate (BTO) membrane, a perovskite oxide thin film that can be epitaxially lifted off and transferred onto a silicon platform. By engineering the device structure and epitaxy process, polarization asymmetry is introduced in capacitance-voltage characteristics. The resulting BTO-based FeCAP exhibits superior memory behavior, including a wide memory window of 308 picofarads and a low switching field of 0.005 megavolts per centimeter, outperforming conventional hafnia-based FeCAPs. Furthermore, these properties are preserved after active layer transfer onto a silicon platform. This approach provides a viable pathway for high-quality BTO to integrate into industry-compatible processes and to drive progress in future logic/memory applications.