Physical unclonable functions (PUFs) should exhibit unique and highly reliable key values. However, commonly reported PUF architectures involve entropy sources sensitive to small environmental perturbations that produce unsteady final key responses. Here we report a stable PUF bitcell that overcomes sensitivity challenges by using the capacity to fuse back the random generated key values into the PUF itself constituted as a non-volatile random access memory (NVR). The proposed PUF bitcell is based on floating gates (FG) NVR cells implemented in a standard CMOS technology without additional masks or fabrication steps. Measurement results from a fabricated PUF macro in a 0.18μm CMOS node indicate an average less than 3% unstable bits for bitcells without post-processing. PUF key bits of programmed cells are 100% stable after applying the UP/DOWN-count stabilization scheme.