The ionic polymerization of acetylene in cold plasmas of C2H2/He and C2H2/Ar has been experimentally studied and modeled in radio frequency (rf) discharges with conditions selected to avoid particle formation. Steady-state distributions of positive and negative ions were measured with mass spectrometry. All the measured distributions are dominated by ions with an even number of carbon atoms, reflecting the characteristic polyyne structures typical for the polymerization of acetylene. The distributions show a monotonic decrease in intensity from ions with two carbon atoms until the highest number of atoms detected. For cations, the distributions extend until 12 carbon atoms. The anion distributions extend further, and negative ions with 20 C atoms are observed in the C2H2/Ar plasma. From the measured mass spectra it is not possible to decide on the possible presence of aromatic species in ions with more than six carbon atoms. A simple model assuming a homogeneous discharge was used to describe the plasma kinetics and could account for the measured ion distributions with reasonable values of charge density and electron temperature. The results of this work stress the important role of the vinylidene anion and indicate that Ar and He do not have much influence on the carbon chemistry.