The stochastic switching mechanism and intrinsic variability of resistive random access memory (RRAM) present severe challenges for memory applications, which, however, may be utilized to implement the physical unclonable function (PUF) for hardware security. A PUF based on RRAM resistance variability is proposed in this letter. Unlike PUFs based on manufacturing variation, this proposal exploits an intrinsic variability in physical mechanisms with reconfigurability. Key characteristics of the PUF design are assessed by simulation using measured RRAM properties and device model. Truly random variation of RRAM resistance is critical for PUF uniqueness (or unclonability). The reliability (or robustness) of the proposed PUF is affected by temperature and voltage dependence of RRAM resistance as well as retention characteristics. Large separation between inter-chip and intra-chip Hamming distance as the measure of uniqueness and reliability confirms the feasibility of the PUF proposal.