  We study the twisted local zeta function associated to a polynomial in two
variables with coefficients in a non-Archimedean local field of arbitrary
characteristic. Under the hypothesis that the polynomial is arithmetically non
degenerate, we obtain an explicit list of candidates for the poles in terms of
geometric data obtained from a family of arithmetic Newton polygons attached to
the polynomial. The notion of arithmetical non degeneracy due to Saia and
Z\'u\~niga-Galindo is weaker than the usual notion of non degeneracy due to
Kouchnirenko. As an application we obtain asymptotic expansions for certain
exponential sums attached to these polynomials.
