After training in Cape Town as a zoologist, Robinson moved to Pretoria in 1946 to take up a post at the Transvaal Museum. In Pretoria, he worked with Robert Broom. They focused on excavations at the caves of Sterkfontein, Kromdaai and Swartkrans. Between 1946 and 1952 they jointly published twenty-three books and articles.
After Broom's death in 1951, Robinson took over as head of the Department of Vertebrate Paleontology and Physical Anthropology. In 1956 he published what is arguably his most important work, a monograph titled The Dentition of the Australopthecinae after which the University of Cape Town awarded him a Doctor of Science degree.
In 1963 Robinson began a Professorship at the University of Wisconsin-Madison. He was a gifted teacher and taught courses in evolutionary theory and human origins, zoology and anthropology. Robinson continued to make trips back to South Africa to carry out research.
He died in Madison, Wisconsin in 2001.