In the context of f(R) theories of gravity, we address the problem of finding
a rotating charged black hole solution in the case of constant curvature. The
new metric is obtained by solving the field equations and we show that the
behavior of it is typical of a rotating charged source. In addition, we analyze
the thermodynamics of the new black hole. The results ensures that the
thermodynamical properties in f(R) gravities are qualitatively similar to those
of standard General Relativity.Comment: 9 pages, no figure