In this paper, an artificial neural network (ANN) based surrogate modeling is performed to estimate the variability in multilevel spin-orbit torque magnetic random-access memory (SOT-MRAM). ANN is utilized to predict the impact of variations in device parameters such as oxide thickness, free layer thickness, tunnel magneto-resistance (TMR), and temperature on the resistance and write energy (Ewrite). The results demonstrate that the ANN approach is suited for fast computation when compared with Monte-Carlo framework offering a thousand orders of speedup in magnitude with 99.5%, 98.98%, 98.59%, and 97.99% accuracy respectively for different resistance values (R00, R01, R10, R11).