President Carter yesterday declared a drought emergency in 16 Virginia counties that are parched from the worst drought to hit the state since 1930.

Carter issued the declaration at the request of Virginia Gov. Mills E. Godwin, who had declared a state of emergency in the counties on July 7.

The declaration will provide drought-stricken dairy farmers and cattle ranchers with federal money to buy as much as 50 per cent of the feed grain necessary to preserve their "foundation herds" of cattle. The assistance is designed to save farmers from the necessity of selling off their entire herds for slaughter in the face of mounting feed bills.

The 16 counties designated by Thomas P. Dunne, administrator of the Federal Disaster Assistance Administration (FDAA) as being eligible for the federal aid are Augusta, Clarke, Culpeper, Fauquier, Fluvanna, Frederick, Greene, Louisa, Madison, Page, Prince William, Rappahannock, Rockingham, Shenandoah, Stafford and Warren.

The hot dry skies that have scorched the state throughout the summer may mean a loss of more than $106 million to Virginia farmers this year, according to reports submitted to state agricultural officials. Empty silos and fields of stunted corn are an integral part of the landscape in the counties most affected by the drought. With the parched earth unable to provide the grains and hay needed to feed their herds, farmers have been forced to buy grain from places as far away as Idaho or to send their cattle to slaughter much earlier than planned.

According to an FDAA spokesman, the federal assistance available under the drought emergency legislation will enable farmers only to keep their breeder stock - those cattle necessary to assure the continuation of the herd - alive on a "subsistence level" diet.

The emergency funds, which will be provided from the President's Disaster Relief Fund, will not enable farmers to fatten up cattle destined for the marketplace or to enrich the diet of dairy cows to increase the butterfat content of their milk.

The President's action followed a decision last week by a committee of federal agencies to declare 56 Virginia counties and 23 cities eligible for a variety of loan and grant programs to help deflect some of the drought's worst effects.

Under the plan put together by the Interagency Drought Emergency Coordinating Committee, farmers in the designated areas can apply for 5 per cent loans from the Farmers Home Administration to cover prospective crop and livestock losses.

Businessmen affected by the drought are also eligible for loans to cover their losses, while many communities, including all of the Northern Virginia jurisdictions, are eligible for loan and grant programs to help them increase the water supplies in their communities.

The President's action was the 22d such declaration of a drought emergency in the last 13 months. At least 14 states have so far received $111 million in federal funds to fight the drought's devastating effects during the last year.