  We prove that any smooth projective geometrically connected non-isotrivial
curve of genus $g\ge 2$ over a function field of any characteristic has at most
$112g^2+240g+380$ torsion points for any Abel-Jacobi embedding of the curve
into its Jacobian. The proof basically uses Zhang's admissible pairing on
curves, the arithmetic Hodge index theorem for function fields and the metrized
graph analogue of Elkie's lower bound for the Green function.
