Background:The γ process in supernova explosions is thought to explain the origin of proton-rich isotopes between Se and Hg, the so-called p nuclei. The majority of the reaction rates for γ process reaction network studies have to be predicted in Hauser-Feshbach statistical model calculations using global optical potential parametrizations. While the nucleon + nucleus optical potential is fairly well known, for the α + nucleus optical potential several different parametrizations exist and large deviations are found between the predictions calculated using different parameter sets. Purpose: By the measurement of elastic α-scattering angular distributions at energies around the Coulomb barrier a comprehensive test for the different global α + nucleus optical potential parameter sets is provided. Methods: Between 20 • and 175 • complete elastic alpha scattering angular distributions were measured on the 113 In p nucleus with high precision at E c.m. = 15.59 and 18.82 MeV. Results: The elastic scattering cross sections of the 113 In(α,α) 113 In reaction were measured for the first time at energies close to the astrophysically relevant energy region. The high precision experimental data were used to evaluate the predictions of the recent global and regional α + nucleus optical potentials. Parameters for a local α + nucleus optical potential were derived from the measured angular distributions. Conclusions: Predictions for the reaction cross sections of 113 In(α, γ ) 117 Sb and 113 In(α,n) 116 Sb at astrophysically relevant energies were given using the global and local optical potential parametrizations.