The Arlington County Board committed itself to an eight-cent reduction in its real estate tax rate yesterday, but the cut will not be enough to offset the increase in property values.

The board agreed to advertise a rate of $1.21 per $100 of assessed property value. Because of a 17 percent increase in values over the last year, most county homeowners' property tax bills will rise by an average of 9.7 percent.

This is what the new tax rate will mean for the average house in the county: valued at $73,250 in January 1979, that house is now worth $85,700. The tax on the house last year was $945 when the rate of assessment was $1.29. This year, the tax will be $1,037 at the $1.21 rate.

Under Virginia law, the board is required to advertise the tax rate before presenting county residents with their tax bills, which are due May 15. The advertisement must tell people what percentage increase to expect, and board members, always eager to be perceived as tax-cutters, worried yesterday over the negative political effects the advertisement might have.

"People don't get past the fact that we are going to raise their taxes," complained Republican board Chairman Walter Frankland as he scrutinized a copy of the legal notice filled with small type except for the large black legend: "Notice of Tax Increase."

Once the $1.21 rate has been published, the board can lower the rate further if it wants, but may not increase it. Republican board member Steven Detwiler suggested that the rate may be set at $1.19 at the end of a public hearing on the issue, which is scheduled for March 15.

Last year, the Republican-dominated board prevented real estate taxes from increasing by using a budget surplus to cut the tax rate.

This year, without such a surplus available, it appears unlikely that the board will be able to repeat that feat, county officials say.