Kearney was drafted by the San Francisco Giants in the fourteenth round of the 1977 Major League Baseball Draft out of the University of Texas.[2] He made his major league debut with the Giants late in the 1979 season, but returned to the minor leagues for the following season.[1] Kearney was drafted by the Oakland Athletics from the Giants in the 1980 minor league draft.[3] Kearney's strong throwing arm was made evident in a game against the Tacoma Indians in 1981 when, he threw out five baserunners attempting to steal second base.[4] He was selected as the catcher for the 1981 Pacific Coast League Northern Division All-Star team.[5]
Kearney was traded to the Seattle Mariners before the 1984 season, replacing Rick Sweet as their starting catcher.[3][11] Despite his strong throwing arm, he developed a reputation for poor pitch-calling skills.[12] During the 1984 season, Mariners pitchers Salomé Barojas and Mike Moore both demanded to have Orlando Mercado as their catcher.[13] This lack of pitch-calling skills along with his light-hitting caused the Mariners to trade for veteran catcher Steve Yeager before the 1986 season.[12] Yeager was expected to catch the majority of the Mariners' games however, he had a disappointing season and Kearney would eventually lead the team's catchers by appearing in 81 games.[14] In 1987, he was displaced by Scott Bradley as the Mariners' starting catcher and was released in July of that year after posting a .170 batting average in 51 games.[1][3]