This paper explores the use of continuous-time Fowler-Nordheim (FN) tunneling for implementing self-powered CMOS sensors that can be used to simultaneously measure and time-stamp occurrences of rare signal events. At the core of the proposed design is a floating-gate device where the FN based electron tunneling is induced through the thin gate-oxide and the control gate is used to couple the signal that is being measured and time-stamped. The signal then modulates the shape of the FN tunneling barrier which is captured by the tunneling rate of electrons being stored on the floating-gate. Thus the sensor continuously operates without the need for any external powering and the data from the sensor can be retrieved to reconstruct the occurrence of events offline. The proof-of-concept has been validated using prototypes fabricated in a standard 0.5-μm CMOS process and the measurement results show that less than 100 fJ of sensing energy is required for event recording and time-stamping.