Large planned photometric surveys will discover hundreds of thousands of supernovae (SNe), outstripping the resources available for spectroscopic follow-up and necessitating the development of purely photometric methods to exploit these events for cosmological study. We present a light curve fitting technique for type Ia supernova (SN Ia) photometric redshift (photo-z) estimation in which the redshift is determined simultaneously with the other fit parameters. We implement this "LCFIT+Z" technique within the frameworks of the MLCS2K2 and SALTII light curve fit methods and determine the precision on the redshift and distance modulus. This method is applied to a spectroscopically confirmed sample of 296 SNe Ia from the Sloan Digital Sky Survey-II (SDSS-II) SN Survey and 37 publicly available SNe Ia from the Supernova Legacy Survey (SNLS). We have also applied the method to a large suite of realistic simulated light curves for existing and planned surveys, including the SDSS, SNLS, and the Large Synoptic Survey Telescope. When intrinsic SN color fluctuations are included, the photo-z precision for the simulation is consistent with that in the data. Finally, we compare the LCFIT+Z photo-z precision with previous results using color-based SN photo-z estimates.