This paper introduces the concept of spin-orbit-torque-MRAM (SOT-MRAM) based physical unclonable function (PUF). The secret of the PUF is stored into a random state of a matrix of perpendicular SOT-MRAMs. Here, we show experimentally and with micromagnetic simulations that this random state is driven by the intrinsic nonlinear dynamics of the free layer of the memory excited by the SOT. In detail, a large enough current drives the magnetization along an in-plane direction. Once the current is removed, the in-plane magnetic state becomes unstable evolving towards one of the two perpendicular stable configurations randomly. In addition, an hybrid CMOS/spintronics model is used to evaluate the electrical characteristics of a PUF realized with an array of 16x16 SOT-MRAM cells. Beyond robustness against voltage and temperature variations, hardware authentication based on this PUF scheme has additional advantages over other PUF technologies such as non-volatility (no power consumption in standby mode), reconfigurability (the secret can be rewritten), and scalability. We believe that this work is a step forward the design of spintronic devices for application in security.