Stellar nuclear reactions, generally occurring at energies well below the Coulomb barrier, have extremely low cross sections posing a very difficult task for their determination using the usual prompt γ-ray detection method. We describe here the application of the highly sensitive Accelerator Mass Spectrometry technique (AMS) as an alternative method for the determination of the resonance strengths of the ²⁵Mg(p,γ) reaction, by off-line counting of the produced ²⁶Al nuclei.