A proper estimate of moment magnitude, which is a physical measure of the energy released at an earthquake source, is essential for better seismic hazard assessments in tectonically active regions. Here a coda wave modeling approach that enables the source displacement spectrum modeling of the examined event was used to estimate moment magnitudes of central Anatolia earthquakes. To achieve this aim, three-component waveforms of local earthquakes with magnitudes 2.0 <= M-L <= 5.2 recorded at 69 seismic stations, which were operated between 2013 and 2015 within the framework of the Continental Dynamics-Central Anatolian Tectonics (CD-CAT) passive seismic experiment, were utilized. An inversion on the coda wave traces of each selected single event in the database was performed in five different frequency bands between 0.75 and 12 Hz. The resultant moment magnitudes (M-w coda) exhibit a good agreement with routinely reported local magnitude (M-L) estimates for the study area. Apparent move-out that is particularly significant around the scattered variation of M-L-M-w coda data points for small earthquakes (M-L < 3.5) can be explained by possible biases of wrong assumptions to account for anelastic attenuation and seismic recordings with a finite sampling interval. Finally, I present an empirical relation between M-w coda and M-L for central Anatolian earthquakes.