I show that by assuming a standard Blandford-Konigl jet, it is possible to determine the bulk Lorentz factor and angle to the line of sight of self-similar parsec-scale blazar jets by using five measured quantities: redshift, core radio flux, extended radio flux, the magnitude of the core shift between two frequencies, and apparent jet opening angle. From the bulk Lorentz factor and angle computed with this method, one can compute other jet properties such as the Doppler factor, magnetic field strength, and intrinsic jet opening angle. I use data taken from the literature and marginalize over nuisance parameters associated with the electron distribution and equipartition to compute these quantities, although the errors are large. Results are generally consistent with constraints from other methods. Primary sources of uncertainty are the errors on the core shift measurements and the uncertainty in the electron spectral index.