  We present the first determination of the abundance ratios of $^{13}$C
substitutions of cyanoacetylene (HC$_{3}$N),
[H$^{13}$CCCN]:[HC$^{13}$CCN]:[HCC$^{13}$CN] in Titan's atmosphere measured
using millimeter-wave spectra obtained by the Atacama Large
Millimeter-submillimeter Array. To compare the line intensities precisely,
datasets which include multiple molecular lines were extracted to suppress
effects of Titan's environmental conditions and observation settings. The
[HC$^{13}$CCN]:[HCC$^{13}$CN] and [H$^{13}$CCCN]:[HCC$^{13}$CN}] ratios were
obtained from 12 and 1 selected datasets, respectively. As a result, nearly the
uniform [H$^{13}$CCCN]:[HC$^{13}$CCN]:[HCC$^{13}$CN] abundance ratios as 1.17
($\pm$0.20) : 1.09 ($\pm$0.25) : 1 (1$\sigma$) were derived, whereas previously
reported ratios for interstellar medium (ISM) have shown large anomalies that
may be caused by $^{13}$C concentrations in precursors. The result obtained
here suggests that $^{13}$C concentration processes suggested in the ISM
studies do not work effectively on precursors of HC$_{3}$N and HC$_{3}$N itself
due to Titan's high atmospheric temperature and/or depletion of both $^{13}$C
and $^{13}$C$^+$.
