Frank Ryan, former quarterback for the Cleveland Browns, will become director of athletics at Yale University, effective June 1, it was announced yesterday.

Ryan has been director of information systems for the House of Representatives since 1971, after ending his playing career with the Washington Redskins.

He also will lecture in mathematics at Yale.Ryan, 40, a native of Fort Worth, Tex., earned a bachelor's degree in physics at Rice University in 1958 and a doctorate in mathematics there in 1965, working on the latter while playing pro football.

Ryan is replacing Carmen Cozza, who, forced by the school to choose between the positions, decided to remain football coach at Yale. Cozza briefly became athletic director as well as coach after De Laney Kiphuth retired.

Ryan was drafted from Rice by the Los Angeles Rams, with whom he played from 1958 through 1961. He was traded to the Browns before the 1962 season and was selected for the Pro Bowl three times before joining the Redskins under Vince Lombardi for the 1969 and 1970 seasons.

Ryan led the Browns to the National Football League championship in 1964 with a 27-0 upset of the Baltimore Colts, quarterbacked by Johnny Unitas. Ryan threw three touchdown passes to wide receiver Gary Collins.

He was an associate professor of mathematics at Case Western Reserve University in the offseasons while still playing pro football. He left Case when he was engaged by the House of Representatives.

He is the husband of Joan Ryan, sports columnist for the Washington Post. They have been residing in Chevy Chase, Md., with their four sons.