Binding of proteins and small molecules to RNA involves many electrostatic interactions, which may alter the distribution of ions around the RNA molecule. Here, we use molecular dynamics simulations to investigate how binding of a cyclic peptide mimic of the HIV-1 Tat protein affects the ionic distribution around the HIV-1 TAR RNA element. The calculations reproduce the structural properties observed in NMR studies of TAR and its complex. They also provide insight into the rearrangement of counterions during the molecular recognition events leading to the formation of the protein/RNA complex.