[en] The recent detections of ${}^{36}{\mathrm{A}\mathrm{r}\mathrm{H}}^{+}$ and ${}^{38}{\mathrm{A}\mathrm{r}\mathrm{H}}^{+}$ in the interstellar medium have triggered interest in argonium. This molecular cation has proved to be widespread in our galaxy in the diffuse medium and may serve as a very specific tracer of atomic gas and as a proxy for the cosmic-ray ionization rate. Pure rotational transitions of the two isotopologues detected in the ISM have never been recorded in the laboratory until this work. Here, we report on the first detection of the $J=1\leftarrow <!--\; ???\; -->0$ transition of both ${}^{36}{\mathrm{A}\mathrm{r}\mathrm{H}}^{+}$ and ${}^{38}{\mathrm{A}\mathrm{r}\mathrm{H}}^{+}$ produced in a low-pressure glow discharge. All of the rotational and ro-vibrational transition frequencies available have been analyzed in global multi-isotopologues fit to give a comprehensive set of isotopic independent spectroscopic parameters. These data allow us to compute an improved set of rotational and ro-vibrational rest frequencies to assist astronomical searches of ${}^{}{\mathrm{A}\mathrm{r}\mathrm{H}}^{+}$.