General-purpose graphics processing units (GPGPUs) have the ability to execute hundreds to thousands of threads simultaneously. Extreme multithreading requires a large register file to hold state of executing threads and facilitate context switching. As feature size reduces, power consumption in the large register file becomes a major concern.In this work, we exploit Domain Wall Memory (DWM) which is a spin-based memory to reduce power consumption in register file. DWM is a promising technology and offers non-volatility, high energy efficiency, and high density by storing several bits into the domains of a ferromagnetic wire. However, despite of favourable properties of DMW over SRAM technology, DWM poses a unique challenge that the bits must be accessed serially through shift operations, leading to variable and potentially higher access latencies. To address this challenge, we propose a new predictive shift policy. In this policy, we exploit register locality across threads and predict source and destination operands of instructions. We record history of registers accessed by instructions and shift magnetic domains of DWM tracks for subsequent instructions, speculatively. Over a wide range of applications from NVIDIA CUDA SDK, ISPASS, and Rodinia, our predictive scheme achieves dramatic energy saving over an SRAM register file while changing performance negligibly.