After a year of study, the Fairfax County Board of Supervisors voted 8 to 1 yesterday to move county government headquarters from Fairfax City - where it has been since 1800 - to a 266-acre site two miles to the west.

The board also decided to immediately buy the $5.7 million site, called the Smith-Carney tract, out of the county's current operating funds rather than through the sale of bonds.

Some county officials say the move to the new government center could begin in 1983, but others claim the move will be years later.

Board Chairman John F. Herrity cast the lone negative vote, saying the issue should go to public referendum.

Supervisor Audrey Moore (D-Annandale) voted for the relocation, but joined Herrity to vote against immediate purchase of the site, saying she also favored a public referendum on the question of how to acquire the land.

"It is absolutely necessary to go to the public on this issue, Herrity said. "What we are doing is investing a substantial amount in real estate in Fairfax County."

Other supervisors warned against the delay a referendum would cause, saying the site, located between 1-66 and Lee Highway, would only increase in price. A referendum would be required to construct the center through the sale of bonds.

"This is one of the most important decisions ever put before this board," said Supervisor John P. Shacochis (R-Dranesville). "We are people who are big enough to make a big decisions. I don't think the public expects us to idle away and make this decision sometime in the future."

The move, which would not include the county's courts, is intended to accommodate the growing number of Fairfax County employes, expected to reach 10,000 within 40 years. The county now has about 5,500 employes excluding some 8,000 school personnel.

The county now spends about $1 million a year renting space in 15 different locations in Fairfax City to house administrative employes who cannot fit in the county's 12-story government center called the Massey Building also in the city.