Gravity can give rise to (pseudo)scalar fields—for instance due to torsion. In particular, axions of gravitational origin have been proposed as a minimal and compelling solution to the strong CP problem. In this Letter, we critically examine the feasibility of this proposal. We demonstrate that models in which the scalar field couples to fermionic currents only through derivatives do not yield a satisfactory axion. Moreover, we identify the necessary conditions for generating a gravitational axion through quantum effects, highlighting Weyl-invariant Einstein-Cartan gravity as a promising theoretical setting.