Singer has had a varied career, serving in the armed forces, government, and academia. He designed mines for the U.S. Navy during World War II, before completing his Ph.D. in physics from Princeton University in 1948 and working as a scientific liaison officer in the U.S. Embassy in London. He became a leading figure in early space research, was involved in the development of earth observation satellites, and in 1962 established the National Weather Bureau's Satellite Service Center. He was the founding dean of the University of Miami School of Environmental and Planetary Sciences in 1964, deputy assistant administrator for the Environmental Protection Agency, and chief scientist for the Department of Transportation. He held a professorship with the University of Virginia from 1971 until 1994, and with George Mason University until 2000.

Singer has been an advocate of the skeptical stance in the global warming controversy for a number of years. In 1990 he founded the Science & Environmental Policy Project to promote the skeptical position, and in 2006 was named by the CBC as one of a minority of scientists creating a stand-off that is undermining the global response to climate change. In contrast to the scientific consensus, Singer argues there is no evidence that global warming is attributable to human-caused increases in atmospheric carbon dioxide, and that humanity would benefit if temperatures do rise. He is an opponent of the Kyoto Protocol, and has said of the climate models that scientists use to project future trends that "models are very nice, but they are not reality and they are not evidence."

Singer was born in Vienna, Austria, where his father was a jeweler and his mother a homemaker. When the Nazis invaded, the family fled, Singer leaving on a children's transport train with other Jewish children. He ended up in England, where he lived in Northumberland, working for a time as a teenage optician. Several years later he emigrated to Ohio and became an American citizen in 1944. He received a B.E.E. in electrical engineering from Ohio State University in 1943, and an A.M. in physics from Princeton in 1944. He taught physics at Princeton while he worked on his masters and his doctorate, obtaining his Ph.D. there in 1948 with a thesis on "Extensive Airshowers of Cosmic Rays." His supervisor was John Archibald Wheeler, and his thesis committee included J. Robert Oppenheimer and Niels Bohr.

After his masters, Singer joined the Armed Forces, working for the United States Navy on mine warfare and countermeasures from 1944 until 1946. While with the Naval Ordnance Laboratory he developed an arithmetic element for an electronic digital calculator that he called an "electronic brain." He was discharged in 1946 and joined the Upper Atmosphere Rocket Program at the Johns Hopkins University Applied Physics Laboratory in Silver Spring, Maryland, working there until 1950. He focused on ozone, cosmic rays, and the ionosphere, all measured using balloons and rockets launched from White Sands, New Mexico, or from ships out at sea. Rachel White Scheuering writes that for one mission to launch a rocket, he sailed with a naval operation to the Arctic, and also conducted rocket launching from ships at the equator.

From 1950 to 1953, he was attached to the U.S. Embassy in London as a scientific liaison officer with the Office of Naval Research, where he studied research programs in Europe into cosmic radiation and nuclear physics. While there, he was one of eight delegates with a background in guided weapons projects to address the Fourth International Congress of Astronautics in Zurich in August 1953, at a time when, as The New York Times reported, most scientists saw space flight as thinly disguised science fiction.

The New York Times wrote in 1962 that Singer was one of the first scientists to urge the launching of earth satellites for scientific observation during the 1950s. He designed the first instruments used in satellites to measure cosmic radiation and ozone, and in 1951 or 1952 designed the MOUSE—the Minimal Orbital Unmanned Satellite, Earth. It weighed 100 pounds, and according to the Smithsonian National Air and Space Museum contained Geiger counters for measuring cosmic rays, photo cells for scanning the earth, telemetry electronics for sending data back to earth, a magnetic data storage device, and rudimentary solar energy cells. The Baltimore News Post reported in 1957 that had Singer's arguments about the need for satellites been heeded, the U.S. could have beaten Russia by launching the first earth satellite. He also invented the backscatter photometer ozone-monitoring instrument for early versions of weather satellites.

Singer moved back to the United States in 1953, where he took up an associate professorship in physics at the University of Maryland, and at the same time served as the director of the Center for Atmospheric and Space Physics. Scheuering writes that his work involved conducting experiments on rockets and satellites, remote sensing, radiation belts, the magnetosphere, and meteorites. He developed a new method of launching rockets into space: firing them from a high-flying plane, both with and without a pilot. The Navy adopted the idea, and Singer supervised the project. He received a White House Special Commendation from President Eisenhower in 1954 for his work.

He became one of 12 board members of the American Astronautical Society, an organization formed in 1954 to represent the country's 300 leading scientists and engineers in the area of guided missiles—he was one of seven members of the board to resign in December 1956 after a series of disputes about the direction and control of the group.

In November 1957 Singer and other scientists at the university successfully designed and fired three new "Oriole" rockets off the Virginia Capes. The rockets weighed less than 25 pounds and could be built for around $2000. Fired from a converted Navy LSM, they could reach an altitude of 50,000 feet and had a complete telemetry system to send back information on cosmic, ultraviolet and X-rays. Singer said that the firings placed "the exploration of outer space with high altitude rockets on the same basis, cost-wise and effort-wise, as low atmosphere measurements with weather balloons. From now on, we can fire thousands of these rockets all over the world with very little cost."

In February 1958, when he was head of the cosmic ray group of the University of Maryland's physics department, he was congratulated in a telegram to the president of the university from President Eisenhower for his work in satellite research. In April 1958, he was appointed as a consultant to the House Committee on Astronautics and Space Exploration, which was preparing to hold hearings on President Eisenhower's proposal for a new agency to handle space research, and a month later received the Ohio State University's Distinguished Alumnus Award. He became a full professor at Maryland in 1959, and was chosen that year by the United States Junior Chamber of Commerce as one of the country's ten outstanding young men.