A graduate of the Massachusetts Institute of Technology, Mulliken worked, during World War I and for a few years afterward, in government chemical research. He then studied under the physicist Robert A. Millikan at the University of Chicago, receiving his Ph.D. in 1921. He taught at New York University (1926–28) and then joined the faculty of the University of Chicago (1928–85).

Mulliken began working on his theory of molecular structure (molecule) in the 1920s. He theoretically systematized the electron states of molecules in terms of molecular orbitals. Departing from the idea that electron orbitals for atoms are static and that atoms combine like building blocks to form molecules, he proposed that, when molecules are formed, the atoms' original electron configurations are changed into an overall molecular configuration. Further extending his theory, he developed (1952) a quantum-mechanical theory of the behaviour of electron orbitals as different atoms merge to form molecules.

During World War II Mulliken worked on the Plutonium Project, part of the development of the atomic bomb, at the University of Chicago. In 1955 he served as scientific attaché at the U.S. embassy in London.