After a record-setting NCAA College athletic career with the Arizona State Sun Devils baseball team, Horner bypassed the minor leagues and moved directly to the major leagues where together with Dale Murphy, he formed a power-hitting tandem for the Atlanta Braves teams of the early 1980s.

Horner became a victim of the Major League Baseball collusion scandal of 1986–87 after the courts found that owners had illegally shared information during free agency negotiations seeking to deflate player salaries.

His college career at Arizona State University culminated with being named the first winner of the Golden Spikes Award.

With his nine home runs in 1976 he is tied with Ike Davis (2006) for third all-time by a Sun Devil freshman, two behind Barry Bonds (1983).

In his first game, he belted a home run off future Hall of Fame pitcher Bert Blyleven of the Pirates.

In 1980, Horner batted .268, with 35 home runs and 89 RBIs despite being sidelined for a total of 79 games in both seasons after recurring shoulder and leg injuries.

In August 1983, Horner was hitting .303 with 20 homers and a career-high OBP of .383 when he fractured his right wrist while sliding, missing the last 43 games of the season.

Later in the season, after hitting a record 210 career home runs without a grand slam, Horner finally belted a homer with the bases loaded to give the Braves a 4–2 victory over the Pirates.

)[6] After failing to reach an agreement with an MLB club, Horner signed a $2 million, one-year contract with the Yakult Swallows of Japan's Central League.