The local order of aqueous solutions of rodlike polyelectrolytes is analyzed. It is shown that the scaling of the full width at half-height of the first peak of the static structure factor with the concentration C of polyelectrolyte is similar to the scaling of the peak position of the first maximum: it changes from C-1/3 to C-1/2 as C varies from the dilute to the semidilute regime. This result enables us to estimate the number of ordered next neighbor shells, N, arranged locally around a central particle. It is shown, in goad agreement with Monte Carlo results, that N similar to 1 when the ionic strength of the solution, I, is similar to 10(-7)-10(-5) M and the polyelectrolyte surface charge in the solution, Q, is on the order of hundreds of electrons. This order decreases when I goes to similar to 10(-3)-10(-2) M and Q decreases by 1 order of magnitude.