  We derive present constraints on, and prospective sensitivity to, the
electric dipole moment (EDM) of the top quark ($d_t$) implied by searches for
the EDMs of the electron and nucleons. Above the electroweak scale $v$, the
$d_t$ arises from two gauge invariant operators generated at a scale $\Lambda
\gg v$ that also mix with the light fermion EDMs under renormalization group
evolution at two-loop order. Bounds on the EDMs of first generation fermion
systems thus imply bounds on $|d_t|$. Working in the leading log-squared
approximation, we find that the present upper bound on $|d_t|$ is roughly
$10^{-19}$ $e$ cm for $\Lambda = 1$ TeV, except in regions of finely tuned
cancellations that allow for $|d_t|$ to be up to fifty times larger. Future
$d_e$ and $d_n$ probes may yield an order of magnitude increase in $d_t$
sensitivity, while inclusion of a prospective proton EDM search may lead to an
additional increase in reach.
