Caryle Murphy's article {Style, Jan. 17} on the rise of the civil rights anthem ''We Shall Overcome'' was a correct, albeit incomplete, account of the early evolution of what is today a worldwide theme for oppressed peoples. The song, as adapted in 1947 by Zilphia Horton at Tennessee's Highlander Folk School, was first used in the media by ''labor troubadour'' Joe Glazer, in a 1950 film for the Congress of Industrial Organizations' Textile Workers Union called ''Unions at Work.'' That same year, Mr. Glazer produced and copyrighted an album titled ''Eight New Songs for Labor,'' one of which was the future anthem of the civil rights movement.

That same year, 1950, I produced three dozen radio programs as part of the CIO's southern union-organizing efforts, using ''We Shall Overcome'' as the opening and closing theme. These 15-minute programs were heard on dozens of radio stations in southern states from Texas to Virginia. This marked the first wide-ranging use of this stirring music.

One of those who played the theme on the radio programs was the late Graham Jackson, the Navy petty officer who performed for FDR on visits to Warm Springs, Ga., and whose picture weeping while playing the accordion at FDR's death was featured in a classic photo at the time in Life magazine.

So credit for the first use in the media of ''We Shall Overcome'' belongs to the trade union movement. And, of course, considerable credit should be given to Joe Glazer for his crucial role in introducing the future classic first to Americans and then to the world. RICHARD CONN Washington