Fairfax County voters approved an $18.7 million bond issue yesterday to finance construction of a new county courthouse that will relieve crowding at the existing courthouse, part of which was built in 1800.

Only about one of every 10 county voters turned out for yesterdays referendum. The unofficial returns showed 13,109 (55 per cent of those voting) in favor of the bond issue and 10,569 against it.

Chief Circuit Court Judge Barnard F. Jennings said he was delighted with the result and declared that "a new building is absolutely essential to administering justice."

Had voters rejected the bond issue, Judge Jennings could have ordered the county to go ahead with construction, anyway, and funding would have come from the country's current revenues rather than from long-term borrowing. Proponents of the bond issue had argued that if the county were forced to go ahead and finance construction on this basis, the real estate property tax rate would have to be raised.

Must of the opposition to the bond issue came from the county Taxpayers Alliance whose president, Harley M. Williams, said voters were intimidated by being told that if they failed to support the issue, they would be forced to pay higher taxes.

Circuit Court Clerk James E. Hoofnagle said the county will begin immediately to accept bids on the design of the new courthouse, which is expected to be completed by the fall of 1980.

The existing courthouse at Main Street and Chain Bridge Road has been widely criticized as lacking sufficient space for juries, witnesses, defendants, lawyers, judges, the public and court records, some of which - like the wills of George and Martha Washington - are of considerable historic interest.

The new structure, to be built a block away near the intersection of Chain Bridge Road and Jones Street, will house the Circuit and General District Courts and be connected to the new jail now under construction.

The Juvenile and Domestic Relations Court and some county offices will remain in the original courthouse.