Using a combination of the molecular dynamics simulations and theoretical calculations, we have demonstrated that bending rigidity of biological polyelectrolytes (semiflexible charged polymers) is scale-dependent. A bond-bond correlation function describing a chain's orientational memory can be approximated by a sum of two exponential functions manifesting the existence of the two characteristic length scales. One describes the chain's bending rigidity at the distances along the polymer backbone shorter than the Debye screening length, whereas another controls the long-scale chain's orientational correlations. The short length scale bending rigidity is proportional to the Debye screening length at high salt concentrations and shows a weak logarithmic dependence on salt concentration when the Debye screening length exceeds a crossover Value of kappa(-1)(cr) proportional to (l(B)alpha(2)/l(p))(-1/2) (where l(B) is the Bjerrum length, alpha is the fraction of ionized groups, and l(p) is a bare persistence length). The long-scale chain's bending rigidity has a well-known Odijk-Skolnick-Fixman form with a quadratic dependence on the Debye radius. Simulation results and a theoretical model demonstrate good qualitative agreement.