Salt-free aqueous solutions of fragmented DNA are studied in the isotropic (I) phase in the semidilute regime until the I-cholesteric phase transition by a small-angle X-ray scattering technique (SAXS). The interference peak position q(m) as a function of concentration fits an universal curve with exponent 1/2 for an effective rod length L = 340 Angstrom. The form factor of the DNA fragments is obtained from the less concentrated solution, where interference effects are not present in the measured range, and it is in good agreement with the B form of DNA. The interference curves for the more concentrated solutions are experimentally derived by dividing the corrected SAXS curve by the particle form factor. Modeling of the interference peaks with Gaussian functions compares well with recent theories for interparticle interactions on solution of rodlike polyelectrolytes. The peak broadening beta expressed as beta L in function of concentration also fits universal curve with exponent 1/2. The fitting shows that the short-range order for rods in the semidilute region has a correlation length slightly above first neighbors.