We have surveyed four of the globular clusters in the Fornax dwarf galaxy (clusters 1, 2, 3 and 5) for RR Lyrae stars, using archival F555W and F814W Hubble Space Telescope observations. We identify 197 new RR Lyrae stars in these four clusters, and 13 additional candidate horizontal-branch variable stars. Although somewhat restricted by our short observational baseline, we derive periods and light curves for all of the stars in the sample, and calculate photometric parameters such as mean magnitudes and colours. This is the first time that RR Lyrae stars in the Fornax globular clusters have been quantitatively identified and measured.