  We explore the possibility of measuring nuclear gluon distributions at the
Relativistic Heavy-Ion Collider (RHIC) with $\sqrt{s}=200 \, {\rm GeV}$
proton-nucleus collisions. In addition to measurements at central rapidity, we
consider also observables at forward rapidity, consistent with proposed
upgrades to the experimental capabilities of STAR and sPHENIX. The processes we
consider consist of Drell-Yan dilepton, dijet, and direct photon-jet
production. The Drell-Yan process is found to be an efficient probe of gluons
at small momentum fractions. In order to fully utilize the potential of
Drell-Yan measurements we demonstrate how the overall normalization uncertainty
present in the experimental data can be fixed using other experimental
observables. An asset of the RHIC collider is its flexibility to run with
different ion beams, and we outline how this ability could be taken advantage
of to measure the $A$ dependence of gluon distributions for which the current
constraints are scarce.
