Rectification is a fundamental nonlinear transport process that converts an alternating drive into a direct current. In this work, we propose a general theoretical framework for electric current rectification triggered by a dynamical external drive that couples to an arbitrary well-defined operator of a periodic system, and which in the static limit forbids any steady current. In the dynamical regime, the finite frequency $Ω$ of the time-varying drive breaks time-translation invariance and injects energy into the system, enabling a second-order {\it nonlinear rectified} current that has no static counterpart. This rectification process has two distinct origins: (i) an impurity-scattering-modified distribution function at finite frequency, and (ii) a time-domain anomalous velocity stemming from a dynamical mixed Berry curvature. Both contributions persist when the driving frequency lies well below the optical transition gap. Applying our general theory to a buckled magnetic system subject to an out-of-plane oscillating electric field, we characterize the generated current as a {\it nonlinear magnetoelectric gyrotropic effect} and predict that the induced rectified current is sensitive to the magnetic order, thereby offering a feasible electrical probe of Néel order in non-coplanar antiferromagnets.

7 pages, 3 figures