Eibner attended The Woodlands High School in The Woodlands, Texas, and helped them win the 2006 5A state championship as a junior, with teammate Kyle Drabek. As a senior, Eibner was named 15-5A first-team all-district outfielder. Despite being drafted by the Houston Astros in the fourth round of the 2007 MLB draft, Eibner did not sign and attended the University of Arkansas. As a freshman, Eibner led the team in RBI and had three game-winning hits. For his efforts, Eibner was named to Baseball America's Freshman All-American team in 2008. The following season, Eibner was named SEC Pitcher of the Week for his complete-game one-hit shutout win against the #1 Georgia Bulldogs. Eibner struggled significantly at the plate, with his average dropping to.231 and striking out 60 times. However, when the 2009 Arkansas Razorbacks baseball team reached the College World Series, Eibner hit "one of the most memorable home runs in program history" when he tied an elimination game vs Virginia in the top of the ninth with a two-run home run. Eibner returned for his junior season with the Razorbacks, hitting.333 with 22 home runs. On the mound, Eibner went 3-5 in 58 innings for the Razorbacks in the regular season. In the 2010 Tempe, ArizonaSuper Regional, Eibner hit a game-tying home run with the Razorbacks down to their final strike, extending the game to extra innings where the Razorbacks lost in the 12th. Following the 2010 season, Eibner became the fourth Razorback to be named both a freshman All-American and All-American, including teammate Zack Cox. He was also a John Olerud Award Semifinalist, Second Team All-SEC, and ABCA/Rawlings First Team All-South Region player. In 2008 and 2009, he played collegiate summer baseball with the Wareham Gatemen of the Cape Cod Baseball League.
The Kansas City Royals selected Eibner in the second round of the 2010 MLB draft. In 2013, Eibner played for the Northwest Arkansas Naturals of the Class AATexas League. After the 2015 season, Royals added him to their 40-man roster On May 26, 2016, Royals promoted Eibner to the MLB. He made his MLB debut the following night at Kansas City's Kauffman Stadium, going 1-for-3 and scoring a run while striking out twice in the Royals' 7-5 win over the Chicago White Sox. Facing off against the White Sox on May 28, 2016, the Royals were trailing 7-1 in the 9th inning, but Eibner completed the rally with a walk-off single to win it for the Royals 8-7.
On January 25, 2017, Eibner was traded to the Los Angeles Dodgers, in exchange for Jordan Tarsovich and assigned to the Triple-A Oklahoma City Dodgers to begin the season. The Dodgers called him up to MLB on April 19. After playing in 17 games for the Dodgers, he was returned to the minors where the Dodgers attempted to convert him to a pitcher. However, he injured his elbow and underwent Tommy John surgery, ending his season.On September 1, 2017, he was designated for assignment and released the following day.
