RNA polymerases (RNAPs) are motor enzymes that carry out transcription, a critical step in gene expression and regulation.  During transcription elongation, RNAP tracks the helical groove of DNA, generating (+) DNA supercoiling in front of itself, and (-) DNA supercoiling behind.  However, the impact of DNA supercoiling on transcription and gene regulation is not well understood.  Here, we report direct measurements of transcription under torsion.  Using novel angular optical trap-based assays, we monitored the movement of an individual E. coli RNAP as it introduced and worked against either (+) DNA supercoiling downstream or (-) DNA supercoiling upstream.  We found that RNAP stalled at a mean torque of 11 ± 4 pN·nm, significantly higher than a lower bound previously estimated.  RNAP is thus a powerful torsional motor, capable of generating sufficient torque to change DNA topology and structure (e.g., melt DNA).  Upon torque relaxation, ~ 50% of stalled RNAPs resumed transcription within 90 s. This suggests that a significant fraction of stalled transcription complexes in vivo are able to recover if torsional stress is relaxed either by topoisomerases or through DNA rotation.  Furthermore, when RNAP was subjected to a short pulse of torque, well beyond the stall torque, a majority of RNAPs continued transcription immediately after the pulse, suggesting that RNAP is resilient to transient torque fluctuations.  Additionally, we characterized the torque-velocity relationship.  A resisting torque slowed the forward translocation rate, and increased pause frequency and duration.  Together, these results provide a quantitative framework for understanding how DNA supercoiling regulates gene expression.