RNA–peptide interactions are an important factor in the origin of the modern mechanism of translation and the genetic code. Despite great progress in the bioinformatics of RNA–peptide interactions due to the rapid growth in the number of known RNA–protein complexes, there is no comprehensive experimental method to take into account the influence of individual amino acids on non-covalent RNA–peptide bonds. First, we designed the combinatorial libraries of primordial peptides according to the combinatorial fusion rules based on Watson–Crick mutations. Next, we used high-density peptide arrays to investigate the interaction of primordial peptides with their cognate homo-oligonucleotides. We calculated the interaction scores of individual peptide fragments and evaluated the influence of the peptide length and its composition on the strength of RNA binding. The analysis shows that the amino acids phenylalanine, tyrosine, and proline contribute significantly to the strong binding between peptides and homo-oligonucleotides, while the sum charge of the peptide does not have a significant effect. We discuss the physicochemical implications of the combinatorial fusion cascade, a hypothesis that follows from the amino acid partition used in the work.