We demonstrate that the design of the Sloan Digital Sky Survey (SDSS) filter system and the quality of the SDSS imaging data are sufficient for determining accurate and precise photometric redshifts (``photo-z''s) of quasars. Using a sample of 2625 quasars, we show that photo-z determination is even possible for z<=2.2 despite the lack of a strong continuum break that robust photo-z techniques normally require. We find that, using our empirical method on our sample of objects known to be quasars, approximately 70% of the photometric redshifts are correct to within delta z = 0.2; the fraction of correct photometric redshifts is even better for z>3. The accuracy of quasar photometric redshifts does not appear to be dependent upon magnitude to nearly 21st magnitude in i'. Careful calibration of the color-redshift relation to 21st magnitude may allow for the discovery of on the order of 10^6 quasars candidates in addition to the 10^5 quasars that the SDSS will confirm spectroscopically. We discuss the efficient selection of quasar candidates from imaging data for use with the photometric redshift technique and the potential scientific uses of a large sample of quasar candidates with photometric redshifts.

29 pages, 8 figures, submitted to AJ