The transition from an isotropic to a nematic liquid crystal phase in a solution of charged rodlike molecules is studied under conditions in which the characteristic interaction energy between two rods is small compared with the thermal energy, i.e., w’=Q(2) lambda/(epsilon k(B)TL(2))much less than 1. Here, Q and L are the charge and length of the molecules, lambda is the Debye screening length for the small counterions, epsilon is the permittivity of the solution, k(B) is Boltzmann’s constant, and T is the absolute temperature. A truncated virial expansion that includes only two-rod correlations and a Debye-Huckel-like theory that incorporates many-rod correlations are developed. The electrostatic interactions cause a small perturbation to the phase transition for hard rods as long as w’much less than d/lambda where d is the rod diameter. In the region of parameter space defined by d/lambda much less than w’much less than lambda/L, the orientation-independent component of the electrostatic repulsion leads to a lowering of the concentration difference between the phases and a decrease in the molecular alignment in the nematic phase relative to the results for solutions of uncharged rods. Within this region, the many-rod correlations incorporated in the Debye-Huckel theory decrease the importance of the anisotropic electrostatic interactions and prevent a transition to a highly aligned phase predicted by the virial theory. For w’much greater than d/lambda and w’much greater than lambda/L, the anisotropic electrostatic interactions do become important and a highly aligned nematic phase for which the order parameter is asymptotically close to one is achieved.