  The neutron-capture reaction plays a critical role in the synthesis of the
elements in stars and is important for societal applications including nuclear
power generation and stockpile-stewardship science. However, it is difficult -
if not impossible - to directly measure neutron capture cross sections for the
exotic, short-lived nuclei that participate in these processes. In this Letter
we demonstrate a new technique which can be used to indirectly determine
neutron-capture cross sections for exotic systems. This technique makes use of
the $(d,p)$ transfer reaction, which has long been used as a tool to study the
structure of nuclei. Recent advances in reaction theory, together with data
collected using this reaction, enable the determination of neutron-capture
cross sections for short-lived nuclei. A benchmark study of the
$^{95}$Mo$(d,p)$ reaction is presented, which illustrates the approach and
provides guidance for future applications of the method with short-lived
isotopes produced at rare isotope accelerators.
