Virginia Del. Stephen E. Gordy, a conservative Republican legislator who had been considering retiring from office, became the first candidate yesterday to announce he will seek a seat on the Fairfax County Board of Supervisors in a special election this summer.

Gordy, 66, a state legislator since 1983, said he was encouraged by a telephone survey of 149 Republican voters. He said 37.6 percent of those polled said he would be the strongest candidate the GOP could field in the July 15 election to fill the seat to be vacated by Supervisor James M. Scott.

A Providence District Democrat, Scott announced Monday he would resign June 3 from the nine-member Fairfax County Board.

Gordy said yesterday he was the only one of the Republicans being mentioned as a candidate who had won an election and said he could appeal to "voters across the board."

Forty-five percent of the Republicans in the survey said they were undecided over the Scott seat. Eight percent said that Robert Beers, an aide to Supervisor Thomas M. Davis III (R-Mason), would be the strongest candidate, and 7.4 percent chose Steven A. Armstrong, a computer executive who lost to Scott in 1983. Two percent did not answer Gordy's telephone survey.

Beers dismissed the poll as "meaningless." Although he has not announced his candidacy, Beers said he would soon release a list of 100 Republicans who make up his steering committee.

Armstrong could not be reached for comment yesterday.

No Democrats have announced for the seat, which party leaders say they must retain to assure their chances of regaining control of the county board in the 1987 elections. Republicans hold a 5-to-4 majority.

Fairfax School Board member Kate Hanley, a Democrat, said yesterday she was "extremely optimistic" that she would decide to run. Providence Planning Commission member Rosemarie Annunziata, another Democrat, said she also was considering a race.

Although GOP leaders generally regard Gordy, a retired Army colonel and former school principal, as the front-runner among Republicans, he also faces a number of obstacles. A Norfolk newspaper survey last year ranked him 98th out of 100 state delegates in terms of effectiveness; he defeated a little-known Democratic challenger last November by 98 votes