Fulton was first elected as MSP for Coatbridge and Chryston in May 2016. He was the first SNP MSP to be elected to the constituency.  In 2021 he was re-elected with an increased majority bringing his vote share to 57%.

As the MSP for Coatbridge and Chryston, Fulton and his team have worked on thousands of cases for his constituents. In Parliament, Fulton sits on both the Equalities, Human Rights and Civil Justice Committee and the Criminal Justice Committee. Having been a member of 14 cross-party groups, he currently convenes Shared Parenting, Future of Football in Scotland, Social Work, and Adult Survivors of Childhood Sexual Abuse.