The increasing prevalence of multi-site diffusion-weighted magnetic resonance imaging (dMRI) studies potentially offers enhanced statistical power to investigate brain structure. However, these studies face challenges due to variations in scanner hardware and acquisition protocols. While several methods for dMRI data harmonization exist, few specifically address structural brain connectivity. We introduce a new distribution-matching approach to harmonizing structural brain connectivity across different sites and scanners. We evaluate our method using structural brain connectivity data from three distinct datasets (OASIS-3, ADNI-2, and PREVENT-AD), comparing its performance to the widely used ComBat method and the more recent CovBat approach. We examine the impact of harmonization on the correlation of brain connectivity with the Mini-Mental State Examination score and age. Our results demonstrate that our distribution-matching technique effectively harmonizes structural brain connectivity while maintaining non-negativity of the connectivity values, and produces correlation strengths and significance levels competitive with alternative approaches. Qualitative assessments illustrate the desired distributional alignment across datasets, while quantitative evaluations confirm competitive performance. This work contributes to the growing field of dMRI harmonization, potentially improving the reliability and comparability of structural connectivity studies that combine data from different sources in neuroscientific and clinical research.