Physically Unclonable Function (PUF) is cost effective and reliable security primitives widely used in authentication and in-place secret key generation. With growing research in the area of non-CMOS technologies for memories and circuits, it is important to understand their implications on the design of security primitives. Resistive Random Accessible Memory (RRAM) offers easy integration with CMOS due to minimal changes in the process technology. RRAM also demonstrates resistance variability characteristics due to inherent defects in the conducting filament formed inside the metal oxide layer. RRAM based PUF designs exploit either the probabilistic switching of RRAM or the resistance variability during forming, SET and RESET processes. Memory PUFs using RRAM are typically weak PUFs due to fewer number of Challenge Response Pairs (CRPs). We propose strong arbiter PUF based on 1T-1R bit cell which is obtained from conventional RRAM memory array with minimally invasive changes. Conventional voltage sense amplifier is employed to generate the response. The PUF is simulated using 65nm predictive technology models for CMOS and Verilog-A model for a hafnium oxide based RRAM. The proposed PUF architecture is evaluated for uniqueness, uniformity and reliability and by running NIST benchmarks. It demonstrates mean intra-die Hamming Distance (HD) of 0.13% and inter-die HD of 51.3%, and, passes the NIST tests.