  We present a new complete Near-Infrared (NIR, $JHK_s$) census of RR Lyrae
stars (RRLs) in the globular $\omega$ Cen (NGC 5139). We collected 15,472
$JHK_s$ images with 4-8m class telescopes over 15 years (2000-2015) covering a
sky area around the cluster center of 60x34 arcmin$^2$. These images provided
calibrated photometry for 182 out of the 198 cluster RRL candidates with ten to
sixty measurements per band. We also provide new homogeneous estimates of the
photometric amplitude for 180 ($J$), 176 ($H$) and 174 ($K_s$) RRLs. These data
were supplemented with single-epoch $JK_s$ magnitudes from VHS and with
single-epoch $H$ magnitudes from 2MASS. Using proprietary optical and NIR data
together with new optical light curves (ASAS-SN) we also updated pulsation
periods for 59 candidate RRLs. As a whole, we provide $JHK_s$ magnitudes for 90
RRab (fundamentals), 103 RRc (first overtones) and one RRd (mixed--mode
pulsator). We found that NIR/optical photometric amplitude ratios increase when
moving from first overtone to fundamental and to long-period (P>0.7 days)
fundamental RRLs. Using predicted Period-Luminosity-Metallicity relations, we
derive a true distance modulus of 13.674$\pm$0.008$\pm$0.038 mag (statistical
error and standard deviation of the median)---based on spectroscopic iron
abundances---and of 13.698$\pm$0.004$\pm$0.048 mag---based on photometric iron
abundances. We also found evidence of possible systematics at the 5-10% level
in the zero-point of the PLs based on the five calibrating RRLs whose
parallaxes had been determined with HST
