We use the on-shell S-matrix and form factors to compute anomalous dimensions of higher dimension operators in the Standard Model Effective Field Theory. We find that in many instances, these computations are made simple by using the on-shell method. We first compute contributions to anomalous dimensions of operators at dimension-six that arise at one-loop. Then we calculate two-loop anomalous dimensions for which the corresponding one-loop contribution is absent, using this powerful method.