Schuler received a Bachelor of Science degree from Canisius College in 1946. Three years later he was given a Doctor of Philosophy degree from the University of Notre Dame.
Schuler began his career as an assistant professor of chemistry at Canisius College in 1949. Four years later he took a position of an associate chemist and then a chemist at Brookhaven National Laboratory. There he lead a group studying the effects of radiation on materials, a critical area in the dawn of the nuclear age.
In 1956, Robert was appointed a director of radiation research laboratory at Mellon Institute (nowadays Carnegie-Mellon University), where he worked until 1976. He was also a professor of chemistry at Carnegie-Mellon University.
In 1975, he became a director of radiation research laboratory at the University of Notre Dame and held the position for twenty years. Then Robert served as a professor in chemistry at the same university from 1985 to 2000. He was a visiting professor at the Hebrew University in Israel and was appointed as the prestigious C. V. Raman Professor at the University of Madras in India in 1985.
Schuler was a member of American Association for the Advancement of Science, American Chemical Society, American Physical Society, Chemical Society and Radiation Research Society (president from 1975 to 1976).
On June 18,1952 Robert Schuler married Florence F. Schuler. They had 3 daughters and 2 sons.