UNLESS THE CARTER administration reacts quickly and affirmatively to Fidel Castro's offer this week to release about 3,000 more political prisoners - 80 percent of those he says are still held in Cuban jails - it will be undermining the president's own efforts on their behalf. Mr Carter has been urging President Castro for months to take just this step.Yet his administration has been proceeding so gingerly with the processing of the prisoners the Cubans have previously been willingly to release that it has left itself wide open to criticism even from Mr. Castro. Something is wrong when the Cuban leader can ask with some justifications, "Why, at this time, is the United States resisting a quick resolution of this problem?"

The reason, according to the administration, is that it wants to be sure that those who are admitted to this country were really political prisoners and are not common criminals or terrorists or spies. The concern is legitimate - although it contrasts curiously with the way in which large numbers of Vietnamese refugees were admitted to the country. But the mechanism the administration is using to meet it is not. The way it works is that representatives of the FBI, the immigration service and the State Department examine the records and interview each prisoner before making a recommendation to the attorney general, who decides, personally, which prisoners are to be admitted.

That process led to the admission of the first 46 prisoners in October. Their names had been in the hands of the American government since late August. Since that time, the Castro government has listed 288 more prisoners who want to come to the United States, but the processing team has completed its work on only 72 of them. If Mr. Castro is serious about releasing 3,000 prisoners (more than half of whom want to come here) before mid-1979, that pace is unacceptably slow.

The Justice Department has said it will attempt to speed things up by assigning more personnel to the processing team. But that is not likely to be enough. Shortcuts in this laborious process are needed, and one comes quickly to mind. Cuban refugee groups in this country have been keeping track of political prisoners for two decades. They are as likely as anyone to know who is and who is not a political prisoner. The Justice Department must begin to rely much more heavily on their judgment if the whole program is not to collapse of its own bureaucratic weight.

Given the history of this nation is accepting political refugees, it seems odd that the Carter administration has responded so warily to Mr. Castro's offer. Thousands of refugees down through the decades have come, on their own, to our doors and been admitted with minimal screening. The Cuban prisoners have a special case. By urging Mr. Castro again and again to free these people, with the understanding that most of them want to come to the United States, President Carter has in effect invited them here. The least his administration can now do is to let them in with as little red tape as possible.