The GERmanium Detector Array (Gerda) experiment operated enriched high-purity germanium detectors in a liquid argon cryostat, which contains 0.33% of ³⁶ Ar, a candidate isotope for the two-neutrino double-electron capture (2 ν ECEC) and therefore for the neutrinoless double-electron capture (0 ν ECEC). If detected, this process would give evidence of lepton number violation and the Majorana nature of neutrinos. In the radiative 0 ν ECEC of ³⁶ Ar, a monochromatic photon is emitted with an energy of 429.88 keV, which may be detected by the Gerda germanium detectors. We searched for the ³⁶ Ar 0 ν ECEC with Gerda data, with a total live time of 4.34 year (3.08 year accumulated during Gerda Phase II and 1.26 year during Gerda Phase I). No signal was found and a 90% CL lower limit on the half-life of this process was established T_{1 / 2}> 1.5 · 10 ²² year.