We address the simulation-to-real domain gap in six degree- of-freedom pose estimation (6DoF PE), and propose a novel self-supervised keypoint voting-based 6DoF PE framework, effectively narrowing this gap using a learnable kernel in RKHS. We formulate this domain gap as a distance in high-dimensional feature space, distinct from previ- ous iterative matching methods. We propose an adapter network, that evolves the network parameters from the source domain, which has been trained on synthetic data with synthetic poses, to the target domain, which is trained on real data. Importantly, the real data training only uses pseudo-poses estimated by pseudo-keypoints, and thereby requires no real groundtruth data annotations. Our proposed method is called RKHSPose, and achieves state-of-the-art performance among self-supervised methods on three commonly used 6DoF PE datasets including LINEMOD (+4.2%), Occlusion LINEMOD (+2%), and YCB-Video (+3%). It also compares favorably to fully supervised methods on all six applicable BOP core datasets, achieving within −11.3% to +0.2% of the top fully supervised results.