Scott proposed on Robertson's 30th birthday on August 23 by taking her on a motorcycle ride to Middle Tennessee State University, where the couple first met as students.
Robertson told Country Weekly: "We rode down to Murfreesboro and pulled behind the mass communications building at Middle Tennessee State.
"We walked to the exact spot where we met nine years ago. He surprised me by pulling out a ring and asking me to marry him. I said 'yes' and a lot of laughter and tears followed."
The couple plan to tie the knot next spring.
Carter's Chord have scored a series of hits on the country music chart, including 'Young Love' and 'Different Breed'.
The sibling group, who were discovered by Toby Keith, released their sophomore LP Wild Together in May.
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Listen to Carter's Chord's hit 'Different Breed' below: