The charged and neutral kaon form factors are calculated as a phenomenological application of the QCD Dyson-Schwinger equations. The results are compared with the pion form factor calculated in the same framework and yield \mbox{$F_{K^\pm}(Q^2) > F_{\pi^\pm}(Q^2)$} on \mbox{$Q^2\in[0,3]$~GeV$^2$}; and a neutral kaon form factor that is similar in form and magnitude to the neutron charge form factor. These results are sensitive to the difference between the kaon and pion Bethe-Salpeter amplitude and the $u$- and $s$-quark propagation characteristics.