We present the results of the first calculation of the logarithmic corrections to the QCD contribution to same-sign $W$-pair production, $ppto e^pm u_e mu^pm u_mu jj$, for same-sign charged leptons. This includes all leading logarithmic contributions which scale as $alpha_W^4 alpha_s^{2+k}log^k(hat s/p_perp^2)$. This process is important for the study of electroweak couplings and hence the QCD contributions are usually suppressed through a choice of Vector Boson Scattering (VBS) cuts. These select regions of phase space where logarithms in $hat s/p_perp^2$ are enhanced. While the logarithmic corrections lead to a small change for the cross sections, several distributions relevant for experimental studies are affected more significantly.