  The Chinese Space Station Telescope (CSST) spectroscopic survey plans to
deliver high-quality low-resolution ($R > 200$) slitless spectra for hundreds
of millions of targets down to a limiting magnitude of about 21 mag, covering a
large survey area (17500 deg$^2$) and a wide wavelength range (255-1000 nm by 3
bands GU, GV, and GI). In this work, we use empirical spectra of the Next
Generation Spectral Library to simulate the CSST stellar spectra at $R = 250$,
and investigate their capabilities in measuring radial velocities. We find that
velocity uncertainties depend strongly on effective temperature, weakly on
metallicity for only FGK stars, and hardly on surface gravity. It is possible
to deliver stellar radial velocities to a precision of about $3
\,\mathrm{km}\,\mathrm{s}^{-1}$ for AFGKM stars, and about $10
\,\mathrm{km}\,\mathrm{s}^{-1}$ for OB stars, at signal-to-noise ratio (SNR) of
100. Velocity uncertainties using single GU/GV/GI band spectra are also
explored. Given the same SNR, the GU band performs best, the GV band the second
best, and then the GI band. The effects of spectral normalization and imperfect
template on velocity measurements are investigated and found to be very weak.
The uncertainties caused by wavelength calibration are considered and found to
be moderate. Given the possible precision of radial velocities, the CSST
spectroscopic survey can enable interesting science such as searching for
hyper-velocity stars. Limitations of our results are also discussed.
