Hulse was born in New York City. He was interested in science from an early age. In 1963 he entered the Bronx High School of Science and in 1966 went to Cooper Union college in lower Manhattan. In 1974 Hulse was working as a graduate student at the University of Massachusetts, Amherst, under the supervision of Joseph Taylor. It was arranged that he would spend the summer in Puerto Rico using the Arecibo Radio Telescope to search for pulsars, a type of star first observed by Jocelyn Bell Burnell in 1967. Among several pulsars detected by Hulse one particular example, named 1913+16 in the constellation Aquila, proved to be of special significance.

Hulse initially found that the pulsar had a short period of 0.059 seconds. More detailed examination, however, revealed that the pulse rate was not constant but varied by some 5 microseconds from day to day. At first Hulse suspected a computer fault. But despite writing a new program, the variability remained. Eventually Hulse spotted that the variation was cyclical repeating itself every 7.75 hours.

Such phenomena, Hulse argued, would arise naturally if the pulsar was a binary, orbiting an undetected companion star. This would produce a Doppler effect. That is, when the pulsar travels in its orbit towards the Earth the pulses would be crowded together, giving a greater than average pulse rate; when, however, it traveled away from the Earth the pulses would be more spread out and yield a lower than average frequency.

In collaboration with Taylor, Hulse went on to establish some of the basic properties of the pulsar. It appeared to have a mass equivalent to 2.8 solar masses, was thought to be a neutron star with a diameter no more than 20–30 kilometers, and to have an approaching velocity of 300 kps (kilometers per second) and a receding velocity of 75 kps. For his work in this field Hulse shared the 1993 Nobel Prize for physics with Joseph Taylor.

After completing his work on the pulsar 1913+16 in 1977 Hulse moved to Princeton, abandoned astronomy, and began to work at the Plasma Physics Laboratory.