We study the problem of four-form flux quantization in F-theorycompactifications. We prove that for smooth, elliptically fibered Calabi-Yaufourfolds with a Weierstrass representation, the flux is always integrallyquantized. This implies that any possible half-integral quantization effectsmust come from 7-branes, i.e. from singularities of the fourfold. Wesubsequently analyze the quantization rule on explicit fourfolds with Sp(N)singularities, and connect our findings via Sen's limit to IIB string theory.Via direct computations we find that the four-form is half-integrally quantizedwhenever the corresponding 7-brane stacks wrap non-spin complex surfaces, inaccordance with the perturbative Freed-Witten anomaly. Our calculations on thefourfolds are done via toric techniques, whereas in IIB we rely on Sen'stachyon condensation picture to treat bound states of branes. Finally, we givegeneral formulae for the curvature- and flux-induced D3 tadpoles for generalfourfolds with Sp(N) singularities.