He certainly served during WWII (midshipman at Navy, 1943-1946), and then active duty until his father's death caused his return to Plains in 1953; but I see no combat (link and link). From the second link:

Entertainment was hard to come by in the rural Georgia of the 1930s, and for Jimmy his mother's brother offered a glimpse of the outside world. Uncle Tom Gordy had joined the United States Navy, and sent postcards to the Carters from around the globe. His nephew was fascinated with all the exotic places depicted in the cards and began to tell his parents that someday he'd be in the Navy, too. Before he even entered high school he had written the U.S. Naval Academy in Annapolis, Maryland, to ask for a catalogue. In 1941, he graduated as class valedictorian of his tiny high school.

Navy Career and Marriage

The events of World War II (1939-45) motivated many American patriots like Jimmy to enter the military service. There was stiff competition for admission into Annapolis and thus, Carter flung himself into his coursework, studying for a year at Georgia Institute of Technology in 1942. Carter was admitted to Annapolis in 1943 and graduated in the top ten percent of his class in August 1946, just after the end of the war.
Regards

Mike