  Many charged polymers, including nucleic acids, are locally stiff. Their
bending rigidity -- quantified by the persistence length --, depends crucially
on Coulombic features, such as the ionic strength of the solution which offers
a convenient experimental route for tuning the rigidity. While the classic
Odijk-Skolnick-Fixman treatment fails for realistic parameter values, we derive
a simple analytical formula for the electrostatic persistence length. It is
shown to be in remarkable agreement with numerically obtained Poisson-Boltzmann
theory results, thereby fully accounting for non-linearities, among which
counter-ion condensation effects. Specified to double-stranded DNA, our work
reveals that the widely used bare persistence length of 500\,\AA\ is
overestimated by some 20%
