Physically Unclonable Function (PUF) circuits are finding widespread use due to increasing adoption of IoT devices. However, the existing strong PUFs such as Arbiter PUFs (APUF) and its compositions are susceptible to machine learning (ML) attacks because the challenge-response pairs have a linear relationship. In this paper, we present a Recurrent-Neural-Network PUF (RNN-PUF) which uses a combination of feedback and XOR function to significantly improve resistance to ML attack, without significant reduction in the reliability. ML attack is also partly reduced by using a shared comparator with offset-cancellation to remove bias and save power. From simulation results, we obtain ML attack accuracy of 62% for different ML algorithms, while reliability stays above 93%. This represents a 33.5% improvement in our Figure-of-Merit. Power consumption is estimated to be 12.3µW with energy/bit of ≈ 0.16pJ.