  We use a physically motivated semi-analytic model, based on the mass function
of dark matter halos, to predict the number of radio-loud quasars as a function
of redshift and luminosity. Simple models in which the central BH mass scales
with the velocity dispersion of its host halo as M(bh) sigma(halo)^5 have been
previously found to be consistent with a number of observations, including the
optical and X-ray quasar luminosity functions. We find that similar models,
when augmented with an empirical prescription for radio emission, overpredict
the number of faint (10 micro-Jy) radio sources by 1-2 orders of magnitude.
This translates into a more stringent constraint on the low-mass end of the
quasar black hole mass function than is available from the Hubble and Chandra
Deep Fields. We interpret this discrepancy as evidence that black holes with
masses below 10^7 Msun are either rare or are not as radio-loud as their more
massive counterparts. Models that exclude BHs with masses below 10^7 Msun are
in agreement with the deepest existing radio observations, but still produce a
significant tail of high-redshift objects. In the 1-10GHz bands, at the
sensitivity of 10 micro-Jy, we find surface densities of 100, 10, and 0.3
deg^-2 for sources located at z>6, 10, and 15, respectively. The discovery of
these sources with instruments such as the Allen Telescope Array (ATA),
Extended Very Large Array (EVLA), and the Square Kilometer Array (SKA) would
open a new window for the study of supermassive BHs at high redshift. We also
find surface densities of 0.1 deg^-2 at z > 6 for mJy sources that can be used
to study 21 cm absorption from the epoch of reionization. We suggest that,
although not yet optically identified, the FIRST survey may have already
detected 10^3-10^4 such sources.
