[1] Baker played college football for NCAA Division II Fairmont State University in West Virginia.

Baker played with the Daytona Beach Coconuts in 2012, leading them to a ninth-place finish at the club sevens national tournament.

[8] Baker signed a full-time contract with the U.S. Eagles in July 2014 to join the residency program at the U.S. Olympic Training Center in San Diego, California.

[8][9] Baker made his debut at the 2014 Gold Coast Sevens in Australia, where he entered the U.S. team's first match against Canada as a second-half substitute.

He received the 2017 World Rugby Sevens Player of the Year award, beating out Fiji's Jerry Tuwai and South Africa's Roscko Specman.

Baker was an important part of the U.S. victory at the 2018 USA Sevens, the team's first tournament win on home soil.

He completed this feat in a 33–12 victory match against Scotland during the 2019-20 World Rugby Sevens Series in Los Angeles.

[17] Baker led all players in the Paris Olympics with six total tries and 30 points scored (tied with Fiji's Iowane Teba).