  The leading non-zero electric moment of the nucleon strange-quark vector
current is the mean square strangeness radius, $<r_s^2>$. We evaluate the
lightest OZI-allowed contribution to $<r_s^2>$, arising from the kaon cloud,
using dispersion relations. Drawing upon unitarity constraints as well as
$K^{+}N$ scattering and $e^+e^-\to K\bar{K}$ cross section data, we find the
structure of this contribution differs significantly from that suggested by a
variety of QCD-inspired model calculations. In particular, we find evidence for
a strong $\phi$-meson resonance which may enhance the scale of kaon cloud
contribution to an observable level.
