We analyze the effect of conformational fluctuations of charged flexible polymers in the presence of screening. We find that the fluctuations do not invalidate the classical theory of electrostatic persistence length due to Odijk and to Skolnick and Fixman. We show that there are strong local fluctuations with wavelength smaller than the screening length kappa(-1). These fluctuations significantly decrease the direct distance between two monomers separated by a contour length smaller than kappa(-1), although they do not affect the persistence length on much larger length scales. Our theory accounts for the apparent short persistence length recently reported by Barrat and Boyer.