Martin made her international debut for Scotland in 2010, during the 2010 Women's Rugby World Cup. She made her first start in a 2011 match against Spain. From 2016 to 2018, she was the Scotland captain, and she captained Scotland in three Six Nations Championships. Her first match as captain was the 2016 Six Nations Championship match against England. She missed one game of the 2018 Six Nations Championship with an eye injury. Later in the tournament, she captained Scotland to their first away win against Ireland in 12 years. In 2018, Martin was one of eight players to receive a "2021 contract" from the Scottish Rugby Union. The contract provided financial support until the 2021 Rugby World Cup.