In October 2018 Graham was called up again to the training squad and was then promoted to the main squad. He earned his first cap off the bench against Wales in November 2018.[5] His first international try came in the 2019 Six Nations match against Wales at Murrayfield,[6] and he subsequently scored two tries against England in the Calcutta Cup.[7]
Graham scored four tries in Scotland's 2024 autumn nations series fixture against Fiji as they went on to win 57-17, a game in which he also won player of the match. During the game, he had briefly become Scotland's joint all time leading try-scorer before Duhan van der Merwe pulled ahead again before the final whistle.[10] Graham scored on his next appearance for Scotland against Portugal, to draw level with Duhan van der Merwe once more as Scotland's leading try scorer. [11]