While still a teenager, Ritchie made his first-team debut in October 2014 with an appearance from the replacements' bench in the Pro12 match against Leinster.[3] In January 2021, Ritchie signed the longest deal in Edinburgh's history, with head coach Richard Cockerill describing Ritchie as a future Scotland captain. "“Jamie is an excellent young player with an old head on his shoulders. He has a really bright future ahead of him and we’re delighted he’s signed such a long-term deal. His work-rate is immense but it’s the quality of work within that which sets him apart," Cockerill said.[4]
Ritchie received his first call up to the senior Scotland squad by coach Gregor Townsend in October 2017
for the autumn internationals.[7] Ritchie received his first senior cap against Canada on the 9 June 2018 in a 48–10 victory.[8]
Ritchie was picked in Scotland's 2019 Rugby World Cup squad. However he fractured his cheekbone in the last warm-up match for Scotland against Georgia.[9]
Ritchie received player of the match in Scotland's match against France in the 2020 Six Nations, after getting punched by France prop Mohamed Haouas[10] During this game Mohamed Haouas was sent off for dangerous play in the 37th minute for punching Ritchie.[11] He once again won a 2020 Six Nations player of the match award, this time against Wales in a 14–10 victory.[12] It was Scotland's first win on Welsh soil since 2002.