SINCE her graduation from law school at the age of 22. Sandra Day O'Connor, nominated Tuesday to the U.S. Supreme Court, has made her mark both as a judge and as a Republican. politician in Arizona. Mrs. O'Connor, 51, is a judge on the Arizona Court of Appeals. She was born in 1930, in El Paso, Tex., but she grew up on a cattle ranch in southern Arizona and claims that as her native state. She received a bachelor's degree in economics with "great distinction" from Stanford University in 1950. She earned her law degree two y.ears later, also from Stanford and also with honors. She ranked third in her law class; the person who ranked No. 1 was fellow Westerner William Rehnquist, who has been on the Supreme Court since 19'62. Another classmate was Frank X. Gordon, now an Arizona Supreme Court justice. "SHE'S EXCEPTIONALLY well qualified, with a tremendous background in politics,1' Gordon said after learning of her nomination. She was married to a classmate, John O'Connor, and remained in California while he finished law school. She worked for a time as an assistant district attorney in San Mateo County. She joined the Arizona bar in 1957, practiced briefly in Maryvale, Ariz., and was an assistant attorney general from 1965 to 1969. In 1969, she was appointed to the state senate and subsequently was elected to two terms as a Republican. She was elected majority leader, the first woman to win such a powerful state position. She received 75 per cent of the vote, more than any other