Robinson was an undergraduate student at the University of Cambridge, where she studied natural sciences. She moved to the University of Oxford for her graduate studies, where she investigated pleistocene climate chronology. After completing her doctorate, Robinson moved to California.  She was appointed a postdoctoral fellow at California Institute of Technology. At Caltech, worked alongside Jess Adkins on deep sea corals. The research took her on a cruise in the North Atlantic ocean, where she journeyed in a submarine to undersea mountains. On this trip she collected fossils from the sea floor. She studied 16,000 year old coral fossils from the Southern Ocean. This experience inspired her to explore how the Atlantic Ocean changed during climate transitions. She moved to the Woods Hole Oceanographic Institution, where she was made Associate Scientist.