We compute the real and imaginary parts of the one-loop electroweak contributions to the left and right tensorial anomalous couplings of the tbW vertex in the Standard Model (SM). For both tensorial couplings we find that the real part of the electroweak SM correction is close to 10 of the leading contribution given by the QCD gluon exchange. We also find that the electroweak real and imaginary parts for the anomalous right coupling are almost of the same order of magnitude. The one loop SM prediction for the real part of the left coupling is close to the 3σ discovery limit derived from b→sγ. Besides, taking into account that the predictions of new physics interactions are also at the level of a few percents when compared with the one loop QCD gluon exchange, these electroweak corrections should be taken into account in order to disentangle new physics effects from the standard ones. These anomalous tensorial couplings of the top quark will be investigated at the LHC in the near future where sensitivity to these contributions may be achieved.