Using the Green Bank 100 m telescope and the Nobeyama 45 m telescope, we have observed the rotational emission lines of the three 13C isotopic species of HC3N in the 3 and 7 mm bands toward the low-mass star-forming region L1527 in order to explore their anomalous 12C/13C ratios. The column densities of the 13C isotopic species are derived from the intensities of the J = 5-4 lines observed at high signal-to-noise ratios. The abundance ratios are determined to be 1.00:1.01 +- 0.02:1.35 +- 0.03:86.4 +- 1.6 for [H13CCCN]:[HC13CCN]:[HCC13CN]:[HCCCN], where the errors represent one standard deviation. The ratios are very similar to those reported for the starless cloud, Taurus Molecular Cloud-1 Cyanopolyyne Peak (TMC-1 CP). These ratios cannot be explained by thermal equilibrium, but likely reflect the production pathways of this molecule. We have shown the equality of the abundances of H13CCCN and HC13CCN at a high-confidence level, which supports the production pathways of HC3N via C2H2 and C2H2+. The average 12C/13C ratio for HC3N is 77 +- 4, which may be only slightly higher than the elemental 12C/13C ratio. Dilution of the 13C isotope in HC3N is not as significant as that in CCH or c-C3H2. We have also simultaneously observed the DCCCN and HCCC15N lines and derived the isotope ratios: [DCCCN]/[HCCCN] = 0.0370 +- 0.0007 and [HCCCN]/[HCCC15N] = 338 +- 12.
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