We present a fully differential and spin-dependent t-channel single-top-quark calculation at next-to-leading order (NLO) in QCD including off-shell effects by using the complex mass scheme in the Standard Model (SM) and in the Standard Model Effective Field Theory (SMEFT). We include all relevant SMEFT operators at 1/Λ^2 that contribute at NLO in QCD for a fully consistent comparison to the SM at NLO. In addition, we include chirality flipping operators that do not interfere with the SM amplitude and contribute only at 1/Λ^4 with a massless b-quark. Such higher order effects are usually captured by considering anomalous right-handed Wtb and left-handed Wtb tensor couplings. Despite their formal suppression in the SMEFT, they describe an important class of models for new physics.