  A nonlinear charged version of the (2+1)-anti de Sitter black hole solution
is derived. The source to the Einstein equations is a Born-Infeld
electromagnetic field, which in the weak field limit becomes the (2+1)-Maxwell
field. The obtained Einstein-Born-Infeld solution for certain range of the
parameters (mass, charge, cosmological and Born-Infeld constants) represent a
static circularly symmetric black hole. Although the covariant metric
components and the electric field do not exhibit a singular behavior at r=0 the
curvature invariants are singular at that point.
