The rotational g factors of the hydrogen halides, HX (X = F, Cl,Br,I), and noble gas hydride cations, XH+ (X = Ne,Ar,Kr,Xe), have been calculated at the level of the random phase approximation (RPA) as relativistic four-component linear response functions as well as nonrelativistic linear response functions. In addition, using perturbation theory with the mass-velocity and Darwin operators as perturbations, the relativistic corrections have been estimated as quadratic response functions. It was found that the four-component relativistic calculations give in general a more negative electronic contribution to the rotational g factor than the nonrelativistic calculations with relativistic corrections ranging from 0.2% for HF and NeH+ to 2.9% for XeH+ and 3.5% for HI. The estimates of the relativistic corrections obtained by perturbation theory with the mass-velocity and Darwin operators are in good agreement with the four-component results for HF, HCl, NeH+, and ArH+, whereas for HI, KrH+, and XeH+ they have the wrong sign.