The Federal Aviation Administration will hold a random drawing this week to distribute valuable airport landing rights currently allocated to Braniff International.

The FAA said Friday that it will hand out 255 slots--as landing rights are called--at 36 U.S. airports for a 60-day period. The agency said it would exclude from the drawing 50 of Braniff's slots at Dallas/Fort Worth Regional Airport to reduce air traffic delays there.

It also excluded from the drawing 106 Braniff slots handed out to airlines on an "emergency basis" in the few days following Braniff's suspension of service May 12.

The way in which those slots were doled out has caused a stir in the airline industry. Industry sources complained that Administrator J. Lynn Helms and other FAA officials met behind closed doors and gave out specific routes to airlines that promised to serve them.

The 1978 Airline Deregulation Act was designed to leave the selection of routes to the airlines, based on their individual views of marketplace needs. The FAA has been distributing landing rights since the air traffic controllers strike last August.

Although airlines have been flying and advertising the routes they already got from the FAA, the agency has refused to say how the slots were distributed, which airports were involved, or which airlines got them. Delta Airlines said that it filed a Freedom of Information Act request seeking that data.

The agency said Friday that authority for the slots already distributed, originally for seven days, would be extended to 60 days.

The drawing this week will distribute 57 slots at Dallas/Fort Worth, 25 at Kansas City, 20 at Houston, 16 at San Antonio, 11 at Oklahoma City and smaller numbers at the other airports, including 6 at Washington National.

Carriers first will submit schedule requests; then the random drawing will determine each airline's place in line in the slot allocation process. The FAA said the number of slots that will be allocated to airlines will be limited in each turn. For instance, at an airport with 10 or fewer available Braniff slots, no airline will receive more than 2 in its first crack at them. If 31 or more slots are available at an airport, no airline will receive more than 4 slots each time its turn comes up.

Meanwhile, Michael Callaway, a former Civil Aeronautics Board official, has set up a brokerage service to sell or exchange airport slots at the National Transportation Research Corp. The FAA announced recently that it would allow airlines to buy and sell slots for a 30-day period.

In another development, the CAB has moved to assist laid-off airline workers who might qualify for compensation benefits under provisions of the airline deregulation law. The board said that nine airlines, including Braniff, had "major contractions" in their labor forces over the past 12-month period.

Under labor protection provisions of the law, employes whose companies have cut back their labor force by 7 1/2 percent in a year can qualify for assistance if it can be shown that airline deregulation was the primary cause of the reductions.

Under the law, the Labor Department was directed to draw up regulations to implement the special job-loss compensation benefits program within six month, but they haven't been issued yet. Last week, Air Line Pilots Association President J. J. O'Donnell said he received assurances from Labor Secretary Raymond J. Donovan that the department would implement the law within the next two months.