Generative Adversarial Network (GAN) has emerged as one of the most promising semi-supervised learning methods where two neural nets train themselves in a competitive environment. In this paper, as far as we know, we are the first to present a statistically trained Ternarized Generative Adversarial Network (TGAN) with fully ternarized weights (i.e.-1,0,+1) to massively reduce the need for computation and storage resources in the conventional GAN structures. In the proposed TGAN, the computationally expensive convolution operations (i.e. Multiplication and Accumulation) in both generator and discriminator's forward path are converted into hardwarefriendly Addition/Subtraction operations. Accordingly, we propose a Processing-in-Memory accelerator for TGAN called (PIM-TGAN) based on Spin-Orbit Torque Magnetic Random Access Memory (SOT-MRAM) computational sub-Arrays to efficiently accelerate the training process of GAN within non-volatile memory. In addition, we propose a parallelism technique to further enhance the training efficiency of TGAN. Our device-To-Architecture co-simulation results show that, with almost the same inception score to the baseline GAN with floating point number weights on different data-sets, the proposed PIM-TGAN can obtain ~25.6× better energy-efficiency and 22× speedup compared to GPU platform averagely, and, 9.2× better energy-efficiency and 5.4× speedup over the best processing-in-ReRAM accelerators.