The Minimal R-symmetric Supersymmetric Standard Model (MRSSM) provides a realisation of supersymmetry in which the parameter space is less constrained by the current LHC data than in the simplest supersymmetric scenarios. In the present paper, we obtain the most precise theoretical predictions in the MRSSM for squark production at the LHC, enabling accurate interpretations of LHC data in terms of the MRSSM. We perform threshold resummation of soft gluon corrections to the total cross sections for the production of squark-(anti)squark pairs at the LHC in the MRSSM framework. The resummation is carried out using the direct QCD method and reaches the next-to-next-to-leading-logarithmic (NNLL) accuracy, which requires calculating the one-loop matching coefficients in the relevant production channels. The resummed cross sections are then matched to the available NLO results and evaluated for $\sqrt{S}=13.6$ TeV. Compared with the Minimal Supersymmetric Standard Model (MSSM), the cross sections in the MRSSM can be significantly reduced, implying less stringent limits on squark and gluino masses. Our results carry significant implications for exploring the viability of supersymmetry at the LHC. The results of our calculation are publicly available as a numerical package.