A Doppler broadening thermometry (DBT) instrument is built based on cavity ring-down spectroscopy (CRDS) for precise determination of the Boltzmann constant. Compared with conventional direct absorption methods, the high-sensitivity of CRDS allows to reach a satisfied precision at lower sample pressures, which also reduces the influence due to collisions. By recording the spectrum of C$_2$H$_2$ at 787 nm, we demonstrate a statistical uncertainty of 6 ppm (part per million) in the determined linewidth values by several hours measurement at a sample pressure of 1.5 Pa. The influence on the spectroscopy-determined temperatures has been investigated, including the hidden weak lines overlapped with the selected transition for DBT measurements. The reproducibility has also been examined to be better than 10 ppm, and it indicates that the instrument is feasible for DBT measurement toward a precision at the ppm level.
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