  We present a dispersive analysis with the aim to extract the $\Upsilon$-p
scattering length from $\gamma p \to \Upsilon p$ experiments. In this
framework, the imaginary part of the $\Upsilon$-p forward scattering amplitude
is obtained from $\gamma p \to \Upsilon p$ cross section measurements, and is
constrained at high energies from existing HERA and LHC data. Its real part is
calculated through a once-subtracted dispersion relation, and the subtraction
constant is proportional to the $\Upsilon$-p scattering length. We perform a
feasibility study for $\Upsilon$ photo-production experiments at an
Electron-Ion Collider and discuss the sensitivity and precision that can be
reached in the extraction of the $\Upsilon$-p scattering length.
