Rogers signed his first professional contract with Aberdeen in July 2011 and played regularly for the club’s youth sides. In December 2013, he joined Airdrieonians on loan for a month but returned to the Dons at the end of this short spell.
On 1 August 2014, he signed for Dumbarton on a six-month loan deal after impressing in friendly matches as a trialist. He made his debut in a 1–0 victory over Brechin City and was named the club’s Player of the Month for September 2014. His loan deal was extended on 2 January 2015, until the end of the 2014–15 season. At the end of the season, he scooped the ‘Dumbarton Terrace’ and Baxter Ramsay (club sponsor) Player of the Year awards as well as the prestigious Sonstrust Young Player of the Season accolade. He returned to parent club Aberdeen having made 36 appearances in total for Ian Murray’s side, keeping nine clean sheets.
On 26 June 2015, Rogers moved to Falkirk on a loan deal for the whole of the 2015–16 season. During his loan spell, he was announced as part of the PFA Scotland Championship Team of the Season. In July 2016, Rogers returned to the Falkirk Stadium for a second season-long loan spell.
Rogers’ performances on loan at Dumbarton earned him a call-up to the Republic of Ireland U21 squad for the game against Norway U21s in October 2014. He made his debut as a 60th-minute substitute and did not concede in his time on the pitch. The game finished 4–1 to Norway. He made his first start for the team in a 1–0 defeat to United States U21s.
Rogers received his first call-up to the senior Republic of Ireland side for the 2018 FIFA World Cup qualifiers against Georgia and Moldova in October 2016.