The radiofrequency penetration depth \ensuremath{\lambda}(H,T) of the organic superconductor (BEDT-TTF${)}_{2}$Cu(NCS${)}_{2}$ was studied in the mixed state at moderate fields. The data can be scaled into a single functional form \ensuremath{\Delta}\ensuremath{\lambda}(H,T)=\ensuremath{\Delta}${\ensuremath{\lambda}}^{\mathrm{*}}$(T)f(H/${\mathit{H}}^{\mathrm{*}}$(T)), where ${\mathit{H}}^{\mathrm{*}}$(T)\ifmmode\times\else\texttimes\fi{}(1-t${)}^{3/2}$/t can be identified with a ``depinning'' or ``irreversibility'' line. We show that the scaling features are contained in a theory of vortex motion in a periodic pootential under the influence of thermal fluctuations, which describes the functional form quantitatively. The data for \ensuremath{\Delta}\ensuremath{\lambda}(H=0, T) are governed by the same (vortex) length scale as the finite-field data, suggesting that the zero-field state is not a conventional Meissner state obeying a London relation.