The Arlington County Board yesterday adopted a $296.8 million budget that gives high priority to programs for housing, the foreign-born and fighting crime in high-rise development corridors.

"This is not because we have a rising, horrendous crime rate, but because Arlington is a fast-growing county," said County Board Member Ellen M. Bozman as the board endorsed adding 13 police officers. The new officers will patrol such high-rise work centers as Crystal City, the Rosslyn-Ballston corridor and Shirlington, where residents and employe groups have expressed concern about increasing robberies and car thefts.

The county has a daytime population that equals its resident population of 153,000, Bozman said, and police have had to adapt to "vertical policing, rather than horizontal policing" in high-rise neighborhoods.

Under the budget approved yesterday for the fiscal year beginning July 1, county and school employes will receive 5.2 percent pay raises and an additional step on the pay ladder. The board added two extra steps for the 231 "cops on the beat" as an incentive aimed at stopping officers from transferring to higher-paying jobs in the federal government and other Northern Virginia jurisdictions.

The additions, Board Member Albert C. Eisenberg said, "underscore our commitment to the safety of people and property, despite increasing urbanization."

The board created a coordinator for its programs for persons with limited English proficiency and appropriated $160,000 for adult English-language programs.

Housing programs will be given $556,000 for projects ranging from housing grants to replacing federal cuts in community development block grant programs.

The $296.8 million overall budget, which represents a 9.8 percent increase over the current fiscal year, was approved 4 to 1, with the board's only Republican, Michael E. Brunner, dissenting. As he has during each of his three years on the board, Brunner contended that the board could have cut tax rates more than it did.

Although he praised the new police positions, Brunner protested the addition of 79 jobs throughout the government, some of which will be state-funded.

The board cut the real estate tax rate by a penny last month to 94 cents per $100 assessed value, the lowest in the area. Yesterday, in a unanimous vote, the board reduced the personal property tax rate on cars, boats and office equipment by 15 cents to $4.50 per $100 assessed value, one of the lowest in the area.

The board unanimously cut $600,000 in business license taxes, levies that many businesses consider more onerous than the real estate tax. The exact rates in each of the dozens of business categories covered by the tax, which the state had ordered reduced by $200,000, will be set this fall.

The $296.8 million includes a general operating fund of $242.2 million, an increase of 8.1 percent over the current fiscal year that ends June 30. The difference is made up in federal and state revenue and self-supporting activities.

The board appropriated $65.2 million to operate the school system, a 10.5 percent increase over this year. In addition, the board set aside $1.7 million for school capital projects, a 55 percent increase, and $2.5 million for activities jointly run by the county and the school sys-tem, such as high school swimming pools.

The general fund, most of which is supported by real estate taxes, includes $10.5 million for the county's share of operating the Metro transit system and $8.2 million for capital improvements.

Besides outlays for improvements to local community facilities and parks, there is a heavy emphasis on funds to spruce up the county's appearance through landscaping and hiking and biking trails.

"It's a whole series of things to keep Arlington not only a good place to live and work, but also a pretty place to live and work," said Board Member John G. Milliken.

The board also set aside a $2 million contingency fund to help offset potential losses in federal aid because of the Gramm-Rudman-Hollings balanced budget legislation.

The budget already covers the loss of $3 million in aid from the federal government, most of it in revenue-sharing funds.