Unlike its DNA template, RNA abundance and synthesis rates increase with cell size, as part of a mechanism of cellular RNA concentration homeostasis. Here, we study this scaling phenomenon in human cells by combining genome-wide perturbations with quantitative single-cell measurements. Despite relative ease in perturbing RNA synthesis, we find that RNA concentrations remain highly constant. Systems-level analysis indicates that perturbations that would lead to increased nuclear mRNA abundance result in downregulation of mRNA synthesis. This is associated with reduced levels of several transcription-associated proteins and protein states that are normally coordinated with RNA production in single cells, including RNA polymerase II (Pol II) itself. Acute shut-down of nuclear RNA degradation, elevation of nuclear mRNA levels, and mathematical modelling indicate that mammalian cells achieve RNA concentration homeostasis by an mRNA-based negative feedback on transcriptional activity in the nucleus. Ultimately, this acts to robustly scale Pol II abundance with cell volume and coordinate mRNA synthesis and degradation.