Any degree with the title "Doctor" will allow you to be called "Doctor." The Psy.D. degree, as you may know, stands for "Doctor of Psychology." The Ph.D. degree stands for "Doctor of Philosophy," although the degree is awarded in a particular field such as psychology, sociology, biophysics, chemistry, or philosophy. People with M.D., D.O., D.M.D., D.D.S., O.D., D.P.M, D.P.T., Ed.D., etc., degrees may all be called "Doctor."
In short, John Doe, Psy.D. may be called Dr. Doe.