The QCD axion is one of the most appealing candidates for the dark matter in the Universe. In this article, we discuss the possibility to predict the axion mass in the context of a simple renormalizable grand unified theory where the Peccei-Quinn scale is determined by the unification scale. In this framework, the axion mass is predicted to be in the range $m_a simeq (3 - 13) times 10^{-9} rm{eV}$. We study the axion phenomenology and find that the ABRACADABRA and CASPEr-Electric experiments will be able to fully probe this mass window.