Gov. Juan F. Luis, a 38-year-old independent politician, was sworn in today as the Virgin Islands' third elected governor.

The oath-taking in downtown Charlotte Amalie marked the first of three days of public inaugural ceremonies, first here and then on the islands of St. Croix and St. John. Parades, speeches, receptions and formal balls are planned for a full day on each island, with a public holiday declared for residents to participate.

While the local treasury is strapped for money, $85,000 was transferred from a planned recreational project to pay for the inaugural activities.

Luis and his lieutenant governor, former banker Henry A. Millin, had taken their oaths of office privately but officially on New Year's Day -- the first Monday in January as required by law.

Luis has been governor for a year. He succeeded to the office upon the death 4an. 2, 1978, of Gov. Cyril E. King, who was a founder and head of the territory's third political party, the Independent Citizens Movement (ICM).The territory's Democratic and Republican parties are affiliated with the national political parties.

While Luis has retained his ICM affiliation, his lieutenant governor is a Democrat and the two ran successfully without party identification in a contest against the islands' former delegate to Congress, Democrat Ron deLugo. There was no Republican candidate for governor.

DeLugo is being replaced in the nonvoting congressional slot by Republican Melvin H. Evans, who was the Virgin Islands' last appointed and first elected governor.

Luis is a native of nearby Vieques -- an island off Puerto Rico -- but grew up on St. Croix. A former schoolteacher and personnel officer, he made his political debut in 1972 when he was elected to the local legislature as one of seven St. Croix members. Two years later he was tapped by King to serve as his running mate.

His three-island inauguration at public expense follows a tradition established by his predecessors. In 1970 Evans spent $75,000 for his inauguration. Four years later King spent $65,000.