In this work, we investigate, for the first time, the impacts of single trap induced Random Telegraph Noise (RTN) on the drain current of FinFET devices and the stability of FinFET 6T SRAM cell. For FinFET operating in tied-gate mode, we show that the charged trap located near the bottom of the sidewall channel, at the middle of the channel between source/drain results in most significant impact (worst position). In independent-gate mode, degraded RTN is observed and depends on the relative location of the trap and current conduction path. In addition, our results indicate that the correlation between RTN and fin Line Edge Roughness (fin LER) and Work Function Variation (WFV) is not obvious as compared with the BULK counterpart. For 6T SRAM operating in subthreshold region, single charged trap for each individual cell transistor, placed at the worst position, forms 64 possible combinations and the resulting extreme values of cell stability during READ and WRITE operations are examined for various V dd. Because of the reduced carriers with decreasing supply voltage, the relative importance of RTN on cell stability increases and hinders the cell stability of subthreshold 6T SRAM cell in the vicinity of distribution tail.