American Motors Corp. recorded its first profitable year since 1979 by posting 1984 earnings of $15.5 million on a 90 percent increase in Jeep sales, the auto maker announced yesterday.

The earnings, which amounted to 4 cents a share, compared with a 1983 loss of $146.7 million. Sales rose to $4.2 billion from $3.3 billion.

In the fourth quarter, AMC earned $3.1 million -- with no earnings per share -- compared with $7.4 million (6 cents a share) in the fourth quarter of 1983. Sales slipped to $1.061 billion from $1.097 billion a year earlier.

But while the Big Three raised prices and enjoyed brisk sales of more profitable, larger cars, AMC suffered a 1.6 percent loss in sales of its small cars from 1983 to 1984 -- slipping behind American Honda Motor Co. Inc. to become the fifth-largest domestic auto maker.

Meanwhile, AMC said yesterday that its mid-February sales were 51 1/2 percent below year-earlier levels as U.S. auto makers reported a combined sales drop of 9.7 percent for the period.

Chrysler Corp., which has many sales incentives programs in effect for customers and dealers, posted the best year-to-year gain -- 15.3 percent for the Feb. 11-20 industry reporting period. Ford Motor Co. sales were up 1.3 percent, sales by industry leader General Motors Corp. were off 17.1 percent, Volkswagen of America reported an increase of 2.6 percent, and American Honda Motor Co. Inc. reported its first year-to-year sales falloff since it hit full production of U.S.-made Accords last year -- a decline of 5.5 percent.