  The Veneziano amplitude for the tree-level scattering of four tachyonic
scalar of open string theory has an arithmetic analogue in terms of the p-adic
gamma function. We propose a quantum extension of this amplitude using the
q-extended p-adic gamma function given by Koblitz. This provides a one
parameter deformation of the arithmetic Veneziano amplitude. We also comment on
the dificulty in generalising this to higher point amplitudes.
