Career
Avcıbay moved to Elazığspor in 2000. He has spent his entire career in Turkey, playing for Denizlispor, Altay, Antalyaspor, Adana Demirspor and Konyaspor. He joined Manisaspor on loan during the second half of the 2008-2009 season, before making the move permanent at the end of the season.
In 2012, he joined Kasımpaşa, and was used mainly as a back up to Andreas Isaksson.
Over the two years he was there, he made five appearances for the club Two in the Süper Lig and three in the Türkiye Kupasi.
In 2014, he joined Gaziantep Büyükşehir Belediyespor, and was appointed the club captain upon his arrival.