  A three-dimensional slowly rotating black hole solution in the presence of
negative cosmological constant in the Einstein-power-Maxwell theory is studied.
It is shown that in the small rotation limit the electric field, diagonal
metric function and thermodynamic properties in the small rotation limit are
the same as for static case, whereas the small rotation gives in addition a
non-diagonal metric function and magnetic field which are also small. For these
functions cased by rotation of black hole it was obtained exact integral
solution and analytic asymptotic solution.
