Axions, hypothetical particles proposed as an elegant solution to the "strong CP problem" in the Standard Model, have gained attention as promising dark matter candidates. Consequently, there has been strong interest in understanding their interactions with matter and light under specific conditions. As a predecessor of a work aiming at describing the behaviour of axions in spin-1/2 quantum plasmas, this work investigates a new theory of Axion-Quantum Electrodynamics using quantum field theory techniques, such as functional methods, to understand the fundamental interactions of this model through the derivation of Feynman rules.