This study aims to explore the dependence structure between magnitude and frequency for Turkey earthquake data. In the literature, the Gutenberg Richter (GR) model based on lineer regression is often used to determine this dependence. The dependence structure is evaluated using copula models in this study. Copulas are useful statistical tool for modeling the dependence structure so it does not require assumptions such as linearity and normality. Therefore, as well as GR model, various copula functions are used to determine the magnitude-frequency relationship of earthquakes. An application is given to illustrate that the copulas can be used as alternatives to the GR model. The best copula models are selected by goodness of fit tests. Additionally, the probabilities of earthquake occurrence and the bivariate return periods are estimated for these selected copula models. It is seen that the probabilities of earthquakes occurrence for GR and copula models are almost identical, whereas the return periods based on copula models is more realistic than GR approach.