  We obtained single-phase near-infrared (NIR) magnitudes in the $J$- and
$K$-band for a sample of 33 RR Lyrae stars in the Carina dSph galaxy. Applying
different theoretical and empirical calibrations of the NIR
period-luminosity-metallicity relation for RR Lyrae stars, we find consistent
results and obtain a true, reddening-corrected distance modulus of 20.118 $\pm$
0.017 (statistical) $\pm$ 0.11 (systematic) mag. This value is in excellent
agreement with the results obtained in the context of the Araucaria Project
from NIR photometry of Red Clump stars (20.165 $\pm$ 0.015) and Tip of Red
Giant Branch (20.09 $\pm$ 0.03 $\pm$ 0.12 mag in $J$-band, 20.14 $\pm$ 0.04
$\pm$ 0.14 mag in $K$-band), as well as with most independent distance
determinations to this galaxy. The near-infrared RR Lyrae method proved to be a
reliable tool for accurate distance determination at the 5 percent level or
better, particularly for galaxies and globular clusters that lack young
standard candles, like Cepheids.
