The RNA world hypothesis states that the early evolution of life went through a stage in which RNA served both as genome and as catalyst. The central catalyst in an RNA world organism would have been a ribozyme that catalyzed RNA polymerization to facilitate self-replication. An RNA polymerase ribozyme was developed previously in the lab but it is not efficient enough for self-replication. The factor that limits its polymerization efficiency is its weak sequence-independent binding of the primer/template substrate. Here we tested whether RNA polymerization could be improved by a cationic arginine cofactor, to improve the interaction with the substrate. In an RNA world, amino acid-nucleic acid conjugates could have facilitated the emergence of the translation apparatus and the transition to an RNP world. We chose the amino acid arginine for our study because this is the amino acid most adept to interact with RNA. An arginine cofactor was positioned at ten different sites on the ribozyme, using conjugates of arginine with short DNA or RNA oligonucleotides. However, polymerization efficiency was not increased in any of the ten positions. In five of the ten positions the arginine reduced or modulated polymerization efficiency, which gives insight into the substrate-binding site on the ribozyme. These results suggest that the existing polymerase ribozyme is not well suited to using an arginine cofactor.