Aptsiauri began his rugby career at Lelo Saracens in the capital of his home country, Tblissi. In 2021 he was signed by Pro D2 side Grenoble, making his debut in the following year against SU Agen.[4][5]
He was called up as a late addition to the Georgian squad for the 2023 Rugby World Cup replacing an injured Luka Japaridze.[8] He made his international debut coming off the bench against Fiji.[9]