This work presents the optimized design of a physical unclonable function (PUF) primitive based on the cross-point resistive random access memory (RRAM) array. The randomness of the PUF comes from the resistance variation of RRAM cells in the array. A four-cell selection scheme is proposed to create a large number of challenge-response pairs necessary for achieving a high security level. To analyze the performance of the PUF with respect to uniqueness and reliability, the RRAM cross-point array is fabricated and the device parameters are calibrated from the experimental data. Our study shows that the RRAM PUF can function properly across a wide temperature range without degradation in the performance. However, IR drop due to the interconnect resistance in the array can potentially hamper the performance. To mitigate the effect of IR drop, a reverse scaling rule on the feature size (F) is proposed for RRAM PUF. While this increases the area of the RRAM PUF, it improves the PUF performance significantly. Compared to a conventional SRAM PUF in 45nm node, a RRAM PUF array size of 1024×1024 with relaxed F=200nm has -45% lower area, while offering better robustness against invasive and side-channel attacks.