We have performed the first study of the variable star population of Ursa Major I (UMa I), an ultra-faint dwarf satellite recently discovered around the Milky Way (MW) by the Sloan Digital Sky Survey. Combining time series observations in the B and V bands from four different telescopes, we have identified seven RR Lyrae stars in UMa I, of which five are fundamental-mode (RRab) and two are first-overtone pulsators (RRc). Our V, B-V color-magnitude diagram of UMa I reaches V~23mag (at a signal-to-noise ratio of ~6) and shows features typical of a single old stellar population. The mean pulsation period of the RRab stars <P_ab_>=0.628, {sigma}=0.071 days (or <P_ab_>=0.599, {sigma}=0.032 days, if V4, the longest period and brightest variable, is discarded) and the position on the period-amplitude diagram suggest an Oosterhoff-intermediate classification for the galaxy. The RR Lyrae stars trace the galaxy horizontal branch (HB) at an average apparent magnitude of <V(RR)>=20.43+/-0.02mag (average on six stars and discarding V4), giving in turn a distance modulus for UMa I of (m-M)_0_=19.94+/-0.13mag, distance d=97.3_-5.7_^+6.0^kpc, in the scale where the distance modulus of the Large Magellanic Cloud is 18.5+/-0.1mag. Isodensity contours of UMa I red giants and HB stars (including the RR Lyrae stars identified in this study) show that the galaxy has an S-shaped structure, which is likely caused by the tidal interaction with the MW. Photometric metallicities were derived for six of the UMa I RR Lyrae stars from the parameters of the Fourier decomposition of the V-band light curves, leading to an average metal abundance of [Fe/H]=-2.29dex ({sigma}=0.06dex, average on six stars) on the Carretta et al. (2009, J/A+A/505/117) metallicity scale.