We study the half-form Kahler quantization of a smooth symplectic toric manifold $(X,\omega)$, such that $[ \omega/ 2\pi]- c_{1}(X)/2 \in H^{2}(X,{\mathbb{Z}} )$ and is non-negative. We define the half-form quantization of $(X,\omega)$ to be given by holomorphic sections of a certain Hermitian line bundle $L\to X$ with Chern class $[ \omega/ 2\pi]- c_{1}(X)/2$. These sections then correspond to integral points of a corrected polytope $P_{L}$ with integral vertices. For a suitably translated moment polytope $P_{X}$ for $(X,\omega)$, we have that $P_{L}\subset P_{X}$ is obtained from $P_{X}$ by a one-half inward-pointing normal shift along the boundary. We use our results on the half-form Kahler quantization to motivate a definition of half-form quantization in the singular real toric polarization. Using families of complex structures studied in Baier-Florentino-Mourao-Nunes, which include the degeneration of Kahler polarizations to the vertical polarization, we show that, under this degeneration, the half-form $L^{2}$-normalized monomial holomorphic sections converge to Dirac-delta-distributional sections supported on the fibers over the integral points of $P_{L}$, which correspond to Bohr-Sommerfeld fibers. This result and the limit of the connection, with curvature singularities along the boundary of $P_X$, justifies the direct definition we give for the quantization in the singular real toric polarization. We show that the space of quantum states for this definition coincides with the space obtained via degeneration of the Kahler quantization. We also show that the BKS pairing between Kahler polarizations is not unitary in general. On the other hand, the unitary connection induced by this pairing is flat.