We propose a model to account for the observed ESR-like signal at the Larmor frequency in the current noise scanning tunnel microscope (STM) experiments identifying spin centers on various substrates. The theoretical understanding of this phenomenon, which allows for single spin detection on surfaces at room temperature, is not settled for the experimentally relevant case that the tip and substrate are not spin polarized. Our model is based on a direct tip-substrate tunneling in parallel with a current flowing via the spin states. We find a sharp signal at the Larmor frequency even at high temperatures, in good agreement with experimental data. We also evaluate the noise in presence of an ac field near resonance and predict splitting of the signal into a Mollow triplet.