We study the effect of the gas accretion rate ( $\dot{M}_{\rm accr}$ ) on the radial gas metallicity profile (RMP) of galaxies using the EAGLE cosmological hydrodynamic simulations, focusing on central galaxies of stellar mass M_⋆ ≳ 10⁹ M_⊙ at z ≤ 1. We find clear relations between $\dot{M}_{\rm accr}$ and the slope of the RMP (measured within an effective radius), where higher $\dot{M}_{\rm accr}$ are associated with more negative slopes. The slope of the RMPs depends more strongly on $\dot{M}_{\rm accr}$ than on stellar mass, star formation rate (SFR), or gas fraction, suggesting $\dot{M}_{\rm accr}$ to be a more fundamental driver of the RMP slope of galaxies. We find that eliminating the dependence on stellar mass is essential for pinning down the properties that shape the slope of the RMP. Although $\dot{M}_{\rm accr}$ is the main property modulating the slope of the RMP, we find that it causes other correlations that are more easily testable observationally: At fixed stellar mass, galaxies with more negative RMP slopes tend to have higher gas fractions and SFRs, while galaxies with lower gas fractions and SFRs tend to have flatter metallicity profiles within an effective radius.