The Fairfax County County Board of Supervisors last night voted to raise board salaries by 23 percent, from $15,000 to $18,455 a year, starting Jan. 1, when a newly elected board is sworn in.

The supervisors stressed their belief that the raise is wtithin President Carter's wage guidelines, since there have been no raises for the board over the past four years.

James P. McDonald, deputy county executive for management and budget, said federal officials assured him "it would be permissible to permit a catch-up" under the guidelines, which generally limit raises to 7 percent a year.

The vote was 8 to 1, with Supervisor Audrey Moore (D-Annandale) opposing the salary increase.

The board also voted 7 to 2 to give additional 4 percent raises in the ensuing four fiscal years, boosting super- visors' pay to $21,589 a year by July 1, 1983.

Moore and Board Chairman John F. Herrity (R) opposed that measure, saying they would accept no more than a 20 percent increase over the four years.

He said later that county employes also got merit raises, which the supervisors didn't.

In introducing the motion to raise the salaries from $15,000 to $18,455, Supervior Alan Magazine (D-Mason) who is not seeking reelection, said the increase is the amount that the supervisors would have received if they had been given the same pay raises that county employes received over the past four years.

McDonald said the "catch-up" would allow the supervisors to increase their salaries by the cost of living increases given county employes the previous four years.

Moore disagreed with McDonald. She said she also had talked with federal officials who said the board "could not consider retroactive cost of living increases."

"There's no way we can consider the cost of living increases for the previous years," said Moore.

Supervisor Joseph Alexander (D-Lee) said the "catch-up" has been used in other jurisdictions.

Magazine called the salary increase "in the best interest of the community" and the expenditure a "fair share" for the board of directors of a half-billion-dollar corporation. The proposed county budget exceeds half a billion dollars.

The proposals to raise the supervisors' pay, pending for two weeks, has angered county teachers, who have threatend a job action if their demand for a 9.4 percent raise is rejected.

The proposed county budget for the fiscal year beginning July 1 calls for giving all county empolyes, including teachers, 5.15 percent raises9

Under the approved raises approved last night, the supervisors will get $19,193 a year in July 1980; $19,961 in July 1981 and $20,759 in July 1982.

Supervisor James Scott (D-Providence) pointed out that the $18,455 a year board salary will still be less than the $18,776 averate teacher's salary in Fairfax.

The supervisors' jobs are generally considered part time. Four of the nine supervisors have additional jobs.