  The term values of all rotational levels of the
$^4$He${_2}^+\,X^+\,^2\Sigma_u^+\,(\nu^+=0)$ ground vibronic state with
rotational quantum number $N^+\le 19$ have been determined with an accuracy of
8 x 10$^{-4}$ cm$^{-1}$ ($\sim{25}$ MHz) by MQDT-assisted Rydberg spectroscopy
of metastable He$_2^*$. Comparison of these term values with term values
recently calculated ab initio by Tung et al. [J. Chem. Phys. 136, 104309
(2012)] reveal discrepancies that rapidly increase with increasing rotational
quantum number and reach values of 0.07 cm$^{-1}$ ($\sim{2.1}$ GHz) at
$N^+=19$.
