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The density of states of the organic superconductor$\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br, measured by scanning tunnelingspectroscopy on \textit{in-situ} cleaved surfaces, reveals a logarithmicsuppression near the Fermi edge persisting above the critical temperature$T_\mathrm{c}$. A soft Hubbard gap as predicted by the Anderson-Hubbard modelfor systems with disorder exactly describes the experimentally observedsuppression. The electronic disorder also explains the diminished coherencepeaks of the quasiparticle density of states below $T_\mathrm{c}$.

Disorder-induced gap in the normal density of states of the organic superconductor $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br