Context. Laboratory measurements and analysis of the microwave and millimeter-wave spectra of potential interstellar molecules are a prerequisite for their subsequent identification by radioastronomical techniques. The spectral analysis provides spectroscopic parameters that are used in the assignment procedure of the laboratory spectra, and that also predict the frequencies of transitions not measured in the laboratory with a high degree of precision.Aims. An experimental laboratory study and its theoretical analysis is presented for 13 C 2 -methyl formate (HCOO 13 CH 3 ) allowing a search for this isotopologue in the Orion molecular cloud. The 13 C 1 -methyl formate (H 13 COOCH 3 ) molecule was also searched for in this interstellar cloud, using previously published spectroscopic data. Methods. The experimental spectra of 13 C 2 -methyl formate were recorded in the microwave and sub-mm energy ranges (4-20 GHz, 8-80 GHz, 150-700 GHz). The spectra were analyzed using the Rho-Axis Method (RAM), which takes the CH 3 internal rotation and the coupling between internal rotation and global rotation into account. Results. Twenty-seven spectroscopic constants of 13 C 2 -methyl formate have been obtained from a fit of 936 transitions of the ground torsional state with a standard (unitless) deviation of 1.08. A prediction of line positions and intensities is also produced. This prediction allowed us to identify 230 13 C 2 -methyl formate lines in the Orion interstellar molecular cloud. We refitted all previously published ground state transitions of the 13 C 1 -methyl formate molecule in order to provide a prediction of its ground state spectrum. 234 lines of 13 C 1 -methyl formate were detected in the Orion interstellar cloud using that prediction.