  Using the Gerasimov-Drell-Hearn sum rule and experimental total cross
sections for photoproduction of $\eta$, $K$ and $\phi$ mesons on the proton, we
obtain upper bounds for the contribution of strange quarks to the anomalous
magnetic moment of the proton, $|\kappa_{s}| \le 0.20 \kappa_{p}$. The proposed
experiments to measure the spin-dependence of the absorption cross section are
expected to lower these bounds considerably. The existing data on $\eta$
production and phenomenological models for $K$ production agree with a negative
sign for $\kappa_{s}$.
