Anheuser-Busch Inc., the nation's biggest beer maker, is about to get a $100,000 bird-watching fee from the taxpayers for the 3 1/2 years it cared for a flock of fugitive parrots for Uncle Sam. This is a very complicated story.

It all started in the fall of 1974. Agents of the federal Fish and Wildlife Service pounced on a shipment of 205 very noisey and colorful Amazon parrots. The birds had been brought into California illegally from Mexico.

While the law was clear that the parrots had to be seized, it did not deal with the reality that a bird in the hand, particularly 205 screaming birds, is a mess. The wildlife service decided it could not handle the parrots (described as greenish and about the size of an overweight pigeon), so it sent out the call for experienced bird-keepers. Enter Anheuser-Busch Inc.

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Wanting only the best for the parrots, some of whom were molting, messing and jabbering constantly, the law enforcement people picked Busch Gardens as the perfect nestingplace. The Van Nuys, Calif., park had a tropical zoo. Zoo officials said they would hold the government's birds. The government said to bill it.

Finally, this April the bird-watching tab arrived. Federal officials said it was for approximately $110,000. Some government aides admitted they had completely forgotten about the parrot stash. They wondered how the 205 birds were getting along, and were there any little ones? In fact, it was explained, the bird population was down to 91. "The decrese in the number of parrots" the government learned, "stemmed from theft, death or escape."

In estimating its bill, Busch Gardens reckoned it cost about 60 cents a day to care for each parrot. There was some haggling over the actual number of birds cared for. But the cost of room and board was not in question.

Finally, the two parties agreed the government owes Anheuser Busch $100,000 for keeping the birds. The Fish and Wildlife Service, which originally captured them, has been authorized to pay that amount. What happens next to the birds is unclear. What is clear is that it would have been cheaper to deport the parrots to Mexico. Even if they all flew first class!