The Arlington County Board decided last night to cut the county's real estate tax rate by at least 7 cents for calendar 1981.

By unanimous vote, the board agreed to advertise the tax rate at $1.05 per $100 of assessed valuation. The exact rate will be set at the board's March 21 meeting when, members indicated, they may try to cut it even more. By law the rate cannot be increased over what is advertised.

County Manager W. Vernon Ford had recommended that the board advertise the rate at $1.07, only five cents below the current rate of $1.12, to give the board more flexibility.

County staff members are predicting at least a 12 percent average increase in real estate assessments, although the precise figure will not be established until mid-February. So despite a cut in the tax rate, most county landowners will still face stiffer tax bills.

The estimates are that those tax bills could be as much as 7 percent higher than last year's. The law requires the board to list such a percentage increase in the tax-rate advertisement and last night set that at 7 percent, although the final increase in tax bills will probably amount to 5 percent or less.

If the 12 percent increase in assessments is on target, the average property owner would find his assessment jumping from about $86,500 to about $96,900 and would have to pay approximately $49 more than the $969 paid last year.

County Board member Walter Frankland proposed the $1.05 rate, one that corresponds to guidelines issued earlier this month for the fiscal 1982 budget.

In calling for tighter fiscal restraints on the board as it continues its budget deliberations, Frankland said, "It's easier to spend money if you have it. The only way we can cut back on our spending is not having the money there to spend."