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