We report an unambiguous detection of the 13CCH and C13CH isotopomers of the ethynyl radical towards the Orion A ridge by identification of their N = 2 → 1 transitions. The observations have been made with the IRAM 30 m telescope at Pico Veleta, Spain. By these measurements, we confirm an earlier tentative detection of four hyperfine components of C13CH with the KOSMA 3 m telescope at Gornergrat, Switzerland. Although uncertainties in the calibration of line intensities are not completely settled, these observations suggest that C13CH might be the more abundant of the two 13C isotopomers. This tentative finding pertains towards the region where the emission of molecular radicals peaks, i.e., northeast of the Kleinmann-Low nebula. Furthermore, the N = 1 → 0 transition of C13CH has been detected in the same region with the SEST 15 m telescope at La Silla, Chile. In combination with the laboratory N = 4 → 3 and N = 5 ← 4 data, we derive improved ground state rotational constants for both species.