Barrett helped the AIG Men's Collegiate All-Americans defeat a combined New Zealand Universities side during the MCAAs' New Zealand Tour in June 2013 with a try. He was also a member of the San Francisco Golden Gate sevens team at the inaugural World Club 7s at Twickenham Stadium in 2013. Barrett scored a try in the USA Rugby Selects' win against Canada at World Rugby's then-developmental Americas Rugby Championship competition in Langford, British Columbia, in 2013.

In the summer of 2014, Barrett earned his first cap with the Men's Eagles against Scotland and continued to appear in all four Eagles matches at Rugby World Cup 2015. In his transition to Sevens, the athlete was named by Men's Eagles Sevens Head Coach Mike Friday as one of the top five players he's coached. As a well rounded rugby player, Barrett also spent time with Gloucester of the Aviva Premiership.

In July 2016, Barrett was named to the 12-man Team USA squad for Rugby Sevens' debut at the Rio 2016 Olympic Summer Games, scoring 20 points in the United States' five matches at Deodoro Stadium.