$NH_4^+(aq)$ is an acid according to the Arrhenius definition.
Work Step by Step
According to the Arrhenius definition, an acid is a substance which produces $H^+$ ions in an aqueous solution. As we can see from the below equation, $NH_4^+(aq) \rightleftharpoons H^+(aq) + NH_3(aq)$ $NH_4^+$ produces $H^+$ ions in aqueous solutions. So it is an acid.