First, we develop a model of counterion condensation on highly charged polyelectrolyte rings. Using the known analytical results for the electrostatic energy of ring formation, a stronger counterion adsorption is anticipated onto a cyclized polyelectrolyte, as compared to the Manning prediction for a straight rod-like polyelectrolyte. This fact ensures a lower energetic cost of polyelectrolyte bending into a ring. In the main part of the work, we investigate the impact of charges on cyclization of short DNA fragments, both theoretically and by computer simulations. An approximate expression for the electrostatically renormalized DNA cyclization probability is proposed that incorporates the electrostatic energies of polyelectrolyte cyclization and dimerization reactions. Depending on concentration of simple salt and chain length, the probability of formation of ideal polyelectrolyte rings can be either electrostatically inhibited or enhanced. The latter effect is quite counter-intuitive. Afterward, simple computer simulations are performed to enumerate the effects of DNA thermal fluctuations onto the electrostatic energies of cyclized and dimerized DNA fragments in solution. Their outcomes support the possibility of electrostatically enhanced polyelectrolyte ring formation reaction in solution. In the end, we discuss some implications of the results obtained for the future DNA cyclization experiments and provide a short analysis of possible DNA-related features neglected in the modeling.