We study the inflationary gravitational wave background induced by Abelian gauge fields generated by non-minimal kinetic and axial couplings to the inflaton. We show that the gravitational wave spectrum is scale invariant and derive its amplitude for generic gauge field coupling parameters, within the slow-roll approximation. We constrain the coupling values and the scale of inflation for which the induced gravitational wave background is observable, while ensuring that back-reaction on the inflationary dynamics remains negligible. We find that a sizeable axial coupling can boost this secondary gravitational wave signal above the standard inflationary background. In the course of our analysis, we also show how to analytically match tensor perturbations across an arbitrary number of eras with different equations of state.
