Affine registration plays a crucial role in PET/CT imaging, where aligning PET with CT images is challenging due to their respective functional and anatomical representations. Despite the significant promise shown by recent deep learning (DL)-based methods in various medical imaging applications, their application to multi-modal PET/CT affine registration remains relatively unexplored. This study investigates a DL-based approach for PET/CT affine registration. We introduce a novel method using Parzen windowing to approximate the correlation ratio, which acts as the image similarity measure for training DNNs in multi-modal registration. Additionally, we propose a multi-scale, instance-specific optimization scheme that iteratively refines the DNN-generated affine parameters across multiple image resolutions. Our method was evaluated against the widely used mutual information metric and a popular optimization-based technique from the ANTs package, using a large public FDG-PET/CT dataset with synthetic affine transformations. Our approach achieved a mean Dice Similarity Coefficient (DSC) of 0.870, outperforming the compared methods and demonstrating its effectiveness in multi-modal PET/CT image registration.