  We report 272 radial velocities for 19 RR Lyrae variables. For most of the
stars we have radial velocities for the complete pulsation cycle. These data
are used to determine robust center--of--mass radial velocities that have been
compared to values from the literature in a search for evidence of binary
systems. Center--of--mass velocities were determined for each star using
Fourier Series and Template fits to the radial velocities. Our center--of--mass
velocities have uncertainties from $\pm0.16$ km s$^{-1}$ to $\pm$2.5 km
s$^{-1}$, with a mean uncertainty of $\pm$0.92 km s$^{-1}$. We combined our
center--of--mass velocities with values from the literature to look for
deviations from the mean center--of--mass velocity of each star. Fifteen RR
Lyrae show no evidence of binary motion (BK And, CI And, Z CVn, DM Cyg, BK Dra,
RR Gem, XX Hya, SZ Leo, BX Leo, TT Lyn, CN Lyr, TU Per, U Tri, RV UMa, and AV
Vir). In most cases this conclusion is reached due to the sporadic sampling of
the center--of--mass velocities over time. Three RR Lyrae show suspicious
variation in the center--of--mass velocities that may indicate binary motion
but do not prove it (SS Leo, ST Leo, and AO Peg). TU UMa was observed by us
near a predicted periastron passage (at 0.14 in orbital phase) but the absence
of additional center--of--mass velocities near periastron make the binary
detection, based on radial velocities alone, uncertain. Two stars in our sample
show $H\gamma$ emission in phases 0.9--1.0: SS Leo and TU UMa.
