OAKLAND, Calif. (AP) _ After a crippling December freeze, the price of oranges is likely to keep rising and the supply may run out, industry watchers say.

''Come February, I don't think you'll see any more navel oranges,'' said Leo Rolandelli, a fruit broker at Jacob, Malcolm and Burtt in San Francisco.

Thirteen straight days of subfreezing cold in the San Joaquin Valley devastated California's navel orange crop, sending prices spiraling upward.

''I was paying $9 a box for navel oranges before the freeze,'' said Steve DelMasso of Bay Cities Produce in Oakland. ''Now they're costing me about $20 a box, and I'm selling them for $22 to $23 a box.''

California produced 2.2 million tons of oranges last year with a market value of $438 million. Up to half of the 1990-91 crop was ruined by frost, according to official estimates.

Despite the shortage, California probably will not lift its ban on overseas citrus, created to protect against agricultural diseases and pests that could harm the state's industry, officials say.

''I don't think the rules will be lifted because of the freeze,'' said Roy Borton, a senior agricultural economist for the Department of Food and Agriculture. ''We'll have to rely on Florida, Arizona and Texas for extra oranges and grapefruit.''

Those states, however, raise mostly seeded Valencia oranges used for making juice, while California grows most of the nation's seedless navel oranges.

DelMasso thinks shoppers will switch to other fruits instead of paying higher prices for oranges.

''Consumers are balking,'' he said. ''Nobody wants to pay $1 for an orange.''