Born in Chalkida, Varkas came through the academy of Olympiacos before moving on to Apollon Smyrnis, making his Super League debut in October 2018 at the age of 20. After the club’s relegation, Varkas helped Apollon win promotion back to the Super League in the 2019/20 season. He would make 42 total appearances with two goals and one assists in three seasons at the club. After productive seasons Chania in 2021/22 and Ilioupoli in 2022/23, Varkas would join Egaleo where he was a key figure over two-and-a-half seasons, making 78 total appearances with 11 goals and seven assists. He signed with AKFC in January 2026.