Absolutely. Climate change is already causing earthquakes and it always has. Land that was located underneath continental glaciation during the Last Glacial Maximum is still rising rapidly every year in a process called isostatic rebound, and this can result in earthquakes. This will, of course, increase as more glaciers melt. The most worrisome result from this is not necessarily the size of the earthquakes, but any corresponding landslides caused by rebound or earthquakes that could result in tsunamis.
Additionally, extraction of groundwater or oil can result in earthquakes as the water is removed and ground must subside. The same applies to oil extraction through traditional wells and fracking. We’ve actually created entire new seismic zones just by extracting the resources we then use to create climate change.
Also, and probably mostly important in the longer term than will majorly impact us, we can expect to see increased volcanic and earthquake activity along the edges of many tectonic plates, as the weight from water that used to be sequestered in glaciers over thick, continental crust is redistributed over thin, oceanic crust. The actual physical increase in weight (and thus pressure) can force water deeper into faults and also speed up subduction, thus resulting in increased earthquake frequency. We aren’t sure exactly how much of an impact this will have because it is extremely hard to measure.