  We consider wetting of a one-dimensional random walk on a half-line $x\ge 0$
in a short-ranged potential located at the origin $x=0$. We demonstrate
explicitly how the presence of a quenched chemical disorder affects the
pinning-depinning transition point. For small disorders we develop a
perturbative technique which enables us to compute explicitly the averaged
temperature (energy) of the pinning transition. For strong disorder we compute
the transition point both numerically and using the renormalization group
approach. Our consideration is based on the following idea: the random
potential can be viewed as a periodic potential with the period $n$ in the
limit $n\to\infty$. The advantage of our approach stems from the ability to
integrate exactly over all spatial degrees of freedoms in the model and to
reduce the initial problem to the analysis of eigenvalues and eigenfunctions of
some special non-Hermitian random matrix with disorder--dependent diagonal and
constant off-diagonal coefficients. We show that even for strong disorder the
shift of the averaged pinning point of the random walk in the ensemble of
random realizations of substrate disorder is indistinguishable from the pinning
point of the system with preaveraged (i.e. annealed) Boltzmann weight.
