At the age of 18, Spencer decided to join the U.S. Navy. He had become interested in wireless communications after learning about the wireless operators aboard the Titanic when it sank. In the Navy he made himself an expert on radio technology: "I just got hold of a lot of textbooks and taught myself while I was standing watch at night." He also subsequently taught himself trigonometry, calculus, chemistry, physics, and metallurgy.

By 1939, Spencer became one of the world's leading experts in radar tube design. Spencer worked at Raytheon, a contractor for the U.S. Department of Defense, as the chief of the power tube division. While working at Raytheon, Spencer developed a more efficient way to manufacture magnetrons, increasing production from 100 to 2600 magnetrons per day. With his reputation and expertise, Spencer helped Raytheon win a government contract to develop and produce combat radar equipment for M.I.T.’s Radiation Laboratory. This was of huge importance to the Allies of World War II and became the military's second-highest priority project during World War II, behind the Manhattan Project. For his work, he was awarded the Distinguished Public Service Award by the U.S. Navy.

The legend is that one day while building magnetrons, Spencer was standing in front of an active radar set when he noticed the candy bar he had in his pocket melted. Spencer was not the first to notice this phenomenon, but he was the first to investigate it. He decided to experiment using food, including popcorn kernels, which became the world's first microwaved popcorn. In another experiment, an egg was placed in a tea kettle, and the magnetron was placed directly above it. The result was the egg exploding in the face of one of his co-workers, who was looking in the kettle to observe. Spencer then created the first true microwave oven by attaching a high-density electromagnetic field generator to an enclosed metal box. The magnetron emitted microwaves into the metal box blocking any escape and allowing for controlled and safe experimentation. He then placed various food items in the box, while observing the effects and monitoring temperatures. There are no credible primary sources that verify this story.

Raytheon filed a U.S. Patent application on October 8, 1945, for a microwave cooking oven..[3] In 1947, the first commercially produced microwave oven was about 6 feet tall, weighed about 750 lbs, and cost about $5,000 (equivalent to $65,529 in 2022). In 1967 the first more affordable, $495 (equivalent to $4,344 in 2022), and reasonably sized (counter-top) Radarange brand microwave oven was made available for sale, produced by Amana (a division of Raytheon).

Spencer became Senior Vice President and a Senior Member of the Board of Directors at Raytheon. He received 300 patents during his career. Originally, a Raytheon facility in Burlington, Massachusetts involved in vacuum tube development and manufacturing was named Spencer Labs after Spencer. This facility was eventually closed. Later, a new building at the Raytheon Missile Defense Center in Woburn, Massachusetts, was named in his honor. Other achievements and awards, besides the Distinguished Public Service Award, included membership of the Institute of Radio Engineers, Fellowship in the American Academy of Arts and Sciences, and an Honorary Doctor of Science from the University of Massachusetts, despite having no formal education.

For his invention, Spencer received no royalties, but he was paid a one-time $2.00 gratuity from Raytheon, the same token payment the company made to all inventors on its payroll at that time for company patents.