  The spectroscopic survey of China's Space Survey Telescope (CSST) is expected
to obtain a huge number of slitless spectra, including more than one hundred
million galaxy spectra and millions of active galactic nuclei (AGN) spectra. By
making use of these spectra, we can measure the Baryon Acoustic Oscillation
(BAO) signals over large redshift ranges with excellent precisions. In this
work, we predict the CSST measurements of the post-reconstruction galaxy power
spectra at $0<z<1.2$ and pre-reconstruction AGN power spectra at $0<z<4$, and
derive the BAO signals at different redshift bins by constraining the BAO
scaling parameters using the Markov Chain Monte Carlo method. Our result shows
that the CSST spectroscopic survey can provide accurate BAO measurements with
precisions higher than 1\% and 3\% for the galaxy and AGN surveys,
respectively. By comparing with current measurements in the same range at low
redshifts, this can improve the precisions by a factor of $2\sim3$, and similar
precisions can be obtained in the pessimistic case. We also investigate the
constraints on the cosmological parameters using the measured BAO data by the
CSST, and obtain stringent constraint results for the energy density of dark
matter, Hubble constant, and equation of state of dark energy.
