  We calculate the leading direct-instanton contributions to the operator
product expansion of the nucleon correlator in a magnetic background field and
set up improved QCD sum rules for the nucleon magnetic moments. Remarkably, the
instanton contributions are found to affect only those sum rules which had
previously been considered unstable. The new sum rules show good stability and
reproduce the experimental values of the nucleon magnetic moments with values
of $\chi$, the quark condensate magnetic susceptibility, consistent with other
estimates.
