The Prince George's County teachers union last night rejected an offer from the school board -- described by a board spokesman as "the best we can do" -- for a 9.1 percent pay increase to be phased in between August of this year and April 1982.

David Graham, the teachers' chief negotiator in the troubled 2-month-old contract talks, said the proposal "shows the arrogance of the school board." The offer was unanimously rejected after it was submitted to the union's Faculty Representatives Council yesterday afternoon, Graham said.

Graham noted " a lot of discussion of strike, a lot of discussion of work to rule" at the council meeting. The union also called on the county's 8,000 teachers to show up at an upcoming board meeting to block adoption of the school system's budget, to wear red armbands on the job and to stage a support rally next week.

Current negotiations -- the two sides have met 22 times so far -- have proven far more difficult than those of past years. Last week, 250 teachers drove past the District Heights home of school board chairman Jo Ann Bell to back their side's demands.

The board's proposal came three days after expiration of a deadline for action imposed by the negotiaing team of the Prince George's County Educators Association, the teachers' union.

According to the board, the average teacher in the county is now paid about $22,500 per year. The proposed 9.1 percent increase, coupled with pay raises teachers would automatically get as they acquire another year's seniority, would raise the average pay by more than $2,600 by April of next year, according to the board.