High reddening near the Galactic plane hampers observations and proper characterization of the globular clusters (GCs) located toward the inner regions of the Milky Way. The VISTA Variables in the Via Lactea (VVV) survey observed the Galactic bulge and adjacent disk for several years, providing multi-epoch, near-infrared images for 41 Galactic GCs. Detecting RR Lyrae variable stars belonging to these GCs will aid in their accurate parameterization. By fully leveraging the astrometric, photometric, and variability VVV catalogs, we searched for RR Lyrae stars associated with GCs. Our selection criteria, based on proper motions, proximity to the cluster centers, and distances inferred from their period-luminosity-metallicity relations, enable us to accurately identify the RR Lyrae population in these GCs and determine color excesses and distances to these poorly studied GCs in a homogeneous manner. Since the VVV catalogs cover from the innermost regions of the GCs to their outskirts, we can provide a comprehensive picture of the entire RR Lyrae population in these GCs. We have discovered significant RR Lyrae populations in two highly reddened Galactic GCs: UKS 1 and VVV-CL160, previously unknown to host RR Lyrae stars. Additionally, we have detected one RR Lyrae candidate in each of Terzan 4 and Terzan 9, also new to RR Lyrae detection. We further confirm and increase the number of RR Lyrae stars detected in 22 other low-latitude Galactic GCs. The RR Lyrae distances place most of these GCs within the Galactic bulge, aligning well with the few GCs in our sample with reliable Gaia or Hubble Space Telescope measurements. However, most of the VVV GCs lack accurate Gaia distances, and literature distances are generally significantly smaller than those derived in this work. As a byproduct of our analysis, we have obtained the proper motions for all the VVV GCs, independently confirming Gaia results, except for two of the most reddened GCs: UKS 1 and 2MASS-GC02.