Ribonucleoside 2',3'-cyclic phosphates (N>p's) are generated by multiple prebiotically plausible processes and are credible building blocks for the assembly of early RNA oligomers. While N>p's can be polymerized into short RNAs by non-enzymatic processes with variable efficiency and regioselectivity, no enzymatic route for RNA synthesis had been described. Here we report such a non-canonical 3'-5' nucleotidyl transferase activity. We engineered a variant of the hairpin ribozyrne to catalyze addition of all four N>p's (2',3'-cyclic A-, G-, U-, and CMP) to the 5'-hydroxyl termini of RNA strands with 5' nucleotide addition enhanced in all cases by eutectic ice phase formation at -7 degrees C. We also observed 5' addition of 2',3'-cyclic phosphate-activated beta-nicotinamide adenine dinucleotide (NAD>p) and ACA>p RNA trinucleotide, and multiple additions of GUCCA>p RNA pentamers. Our results establish a new mode of RNA 3'-5' extension with implications for RNA oligomer synthesis from prebiotic nucleotide pools.