We describe the assignment of a previously unidentified interstellar absorption line to ArH$^+$ and discuss its relevance in the context of hydride absorption in diffuse gas with a low H$_2$ fraction. The column densities along several lines of sight are determined and discussd in the framework of chemical models. The column densities of ArH$^+$ are compared to those of other species, tracing interstellar medium (ISM) components with different H$_2$ abundances. Chemical models are constructed, taking UV radiation and cosmic ray ionization into account. Due to the detection of two isotopologues, $^{36}$ArH$^+$ and $^{38}$ArH$^+$, we are confident about the carrier assignment to ArH$^+$. NeH$^+$ is not detected with a limit of [NeH$^+$]/[ArH$^+$] $le$ 0.1. The derived column densities agree well with the predictions of chemical models. ArH$^+$ is a unique tracer of gas with a fractional H$_2$ abundance of $10^{-4}- 10^{-3}$ and shows little correlation with H$_2$O$^+$, which traces gas with a fractional H$_2$ abundance of $approx $0.1. A careful analysis of variations in the ArH$^+$, OH$^+$, H$_2$O$^+$ and HF column densities promises to be a faithful tracer of the distribution of the H$_2$ fractional abundance, providing unique information on a poorly known phase in the cycle of interstellar matter, its transition from atomic diffuse gas to dense molecular gas traced by CO emission. Abundances of these species put strong observational constraints upon magnetohydrodynamical (MHD) simulations of the interstellar medium, and potentially could evolve into a tool to characterize the ISM. Paradoxically, the ArH$^+$ molecule is a better tracer of ew{almost} purely atomic hydrogen gas than H{sc i} itself, since H{sc i} can also be present in gas with a significant molecular content, but ArH$^+$ singles out gas that is $>99.9$% atomic.
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