Coordination of RNA abundance and production rate with cell size has been observed in diverse organisms and cell populations. However, how cells achieve such 'scaling' of transcription with size is unknown. Here we describe a genome-wide siRNA screen to identify regulators of global RNA production rates in HeLa cells. We quantify the single-cell RNA production rate using metabolic pulse-labelling of RNA and subsequent high-content imaging. Our quantitative, single-cell measurements of DNA, nascent RNA, proliferating cell nuclear antigen (PCNA), and total protein, as well as cell morphology and population-context, capture a detailed cellular phenotype. This allows us to account for changes in cell size and cell-cycle distribution (G1/S/G2) in perturbation conditions, which indirectly affect global RNA production. We also take advantage of the subcellular information to distinguish between nascent RNA localised in the nucleolus and nucleoplasm, to approximate ribosomal and non-ribosomal RNA contributions to perturbation phenotypes. Perturbations uncovered through this screen provide a resource for exploring the mechanisms of regulation of global RNA metabolism and its coordination with cellular states.