FORT WORTH, Texas (AP) _ AMR Corp., parent company of American Airlines, has taken steps to thwart any unfriendly acquirers by adopting a so-called ''poison pill'' shareholders rights strategy.

The corporation's board of directors Thursday declared a dividend distribution of one preferred stock purchase right on each outstanding share of AMR common stock.

Robert L. Crandall, AMR chairman and chief executive officer, said the action guards against anyone's ''abusive tactics'' to gain control of AMR without paying all stockholders a premium.

''They do not prevent a takeover, but should encourage anyone seeking to acquire the company to negotiate with the board prior to attempting a takeover,'' Crandall said.

AMR spokesman Lowell Duncan called the move ''prudent business'' and said it does not stem from any real or anticipated attempt to take over AMR. He said the company had been contemplating such a strategy for nearly a year.

Airline analysts said they knew of no attempts or planned attempts to acquire AMR, holding company for the country's second-biggest airline next to United Airlines. AMR had its most profitable year in 1985, with earnings of $345.8 million, compared with $233.9 million in 1984.

It is the third company in the airline industry to adopt such an anti- takeover strategy this year. The others are USAir, sometimes mentioned as a possible takeover target, and financially troubled Eastern Airlines, in which militant union leaders have called on employees to purchase Eastern stock.

Under AMR's plan, each purchase right will entitle stockholders to buy one one-hundredth of a share of a new series of junior participating preferred stock at an exercise price of $200.

The rights can be used only if a person or group acquires 20 percent or more of AMR's common stock or announces a tender offer that woul result in ownership of 30 percent or more of the common stock, Duncan said.

If AMR is acquired in a merger or other business combination transaction, each right will entitle its holder to buy, at the right's current exercise price, a number of the acquiring company's common shares having a market value at that time of twice the right's exercise price.