Fairfax County school officials, under mounting criticism, last night scrapped their controversial plan to start charging rent for textbooks, which the school system has hitherto provided free.

School Superintendent Linton Deck, in withdrawing the plan to begin charging students up to $30 in textbook rent a year said there have been "unanticipated increases in state aid and overstatement of some expenditure accounts" in his budget proposal. Those, he said, eliminate the need for the $2.75 million the rental fees would have brought in.

Deck made it clear he is not philosophically opposed to textbook rental fees, and noted that a cut in a federal aid might result in reinstatement of the unpopular plan.A reduction in so-called federal impact aid to Washington area schools is considered a likely goal of the Reagan administration -- as it has been of other recent administrations, both Republican and Democratic.

The rental plan seemed destined for a bitter battle on the School Board, which is considering Deck's 1981-82 budget proposal. Several board members criticized it, claiming that renting books to students violated the principles of free public education.

In a surprising move last week, the County Council of PTAs -- usually a strong supporter of the school budget -- voted not to endorse the textbook rental fees. Despite the sudden abandonment of the fees, most speakers at a school budget hearing last night went ahead to tell the board they remain opposed to textbook rentals regardless of federal funding.

"The Virginia Constitution guarantees every child a free public education.

It is our responsibility to see that every child has the necessary educational tools, including textbooks," said Toni McMahon, president of the Council of PTAs.

The book-fee proposal drew praticularly heavy fire at the hearing because it was virtually the only reduction in services included in the $395 million budget proposal. Critics questioned the wisdom of renting school books to children while at the same time allocating $13 million for computer technology and creating 215 new jobs.

The decision to scrap the fee also was popular with some members of the County Board of Supervisors. Sandra Duckworth (D-Mt. Vernon) said Deck "knew the idea would not fly." Nancy K. Falck (R-Dranesville) called the decision "delightful."

Textbook rentals, while alien to most areas of the country, are commonplace in Virginia where 109 of the state's 140 school systems rent textbooks to their students. The fees are not common, however, in affluent Northern Virginia, where only Prince William County charges students to use books.

Recent court challenges to the Prince William County fee system have failed to overturn the provision in Virginia law that allows school systems to rent books. The code does provide free books to families too poor to pay the fee.