The inclusive cross section for the production of charmed D * ± mesons in two-photon processes is measured with the AMY detector at the TRISTAN e + e - collider. D * ± mesons are identified from the distribution of charged-particle transverse momenta relative to the jet axis. A data sample corresponding to an integrated luminosity of 176 pb - 1 at a center-of-mass energy of 58 GeV is used to determine a cross section σ(e + e - → e + e - D * ± X) = 270 ± 49(stat) ± 38(syst) pb. The results are compared with theoretical expectations based on the Vector Meson Dominance, direct quark-parton model, and resolved photon processes.