Typical neural networks are incapable of effectively estimating prediction uncertainty, leading to overconfident predictions. Estimating uncertainty is crucial for safety-critical tasks such as autonomous vehicle driving and medical diagnosis and treatment. Bayesian Neural Networks (BayNNs), which combine the capabilities of neural networks and Bayesian inference, are an effective approach for uncertainty estimation. However, BayNNs are computationally demanding and necessitate substantial memory resources. Computation-in-memory (CiM) architectures uti-lizing emerging resistive non-volatile memories such as Spin- Orbit Torque (SOT) have been proposed to increase the resource efficiency of traditional neural networks. However, training scalable and efficient BayNNs and implementing them in the CiM architecture presents its own challenges. In this paper, we propose a scalable Bayesian NN framework via Subset-Parameter inference and its Spintronic-based CiM implementation. Our method is evaluated on large datasets and topologies to show that it can achieve comparable accuracy while still being able to estimate uncertainty efficiently at up to 70 × lower power consumption and 158.7× lower storage memory requirements.