Low-power applications, such as sensing, are becoming increasingly important and demanding in terms of minimizing energy consumption, driving the search for new and innovative interface architectures and technologies. Carbon nanotube FETs (CNFETs) are excellent candidates for further energy reduction, as CNFET-based digital circuits are projected to achieve an order of magnitude improvement in energy-delay product compared with silicon-CMOS at highly scaled technology nodes. However, carbon nanotubes (CNTs) are inherently subject to imperfections and variations such as those induced by mispositioned and metallic CNTs. These substantial imperfections and variations have prevented the demonstration of complex CNFET circuits until now. This paper presents the first demonstration of a subsystem, which is a complete capacitive sensor interface circuit, implemented entirely using CNFETs that can be fabricated reproducibly in a VLSI-compatible fashion. This is made possible by: 1) a digitally oriented interface architecture and 2) the imperfection-immune design paradigm, which combines design and processing techniques to successfully overcome CNT imperfections and variations. In addition to electrical measurements, we demonstrate correct operation of our CNFET circuitry by interfacing it with a sensor used to control a handshaking robot.