Cytoplasmic poly(A) RNA polymerase that adds successive AMP monomers to the 3′-end of specific RNAs, forming a poly(A) tail (PubMed:15070731, PubMed:31792053). In contrast to the canonical nuclear poly(A) RNA polymerase, it only adds poly(A) to selected cytoplasmic mRNAs (PubMed:15070731). Does not play a role in replication-dependent histone mRNA degradation (PubMed:18172165). Adds a single nucleotide to the 3′ end of specific miRNAs, monoadenylation stabilizes and prolongs the activity of some but not all miRNAs (PubMed:23200856, PubMed:31792053).