Born in Trebinje, Social Research Bosnia and Herzegovina, he started playing with local club FK Leotar which was playing in the Bosnian Premier League. Soon he was spoted s talented youngster and in summer 2009 he was already moving abroad, to Serbia, and signing with New Belgrade-based club FK Bežanija. A former Serbian SuperLiga member, Bežanija was fighting back then in the Serbian First League for it"s return to SuperLiga.
Mrkaić made 14 appearances in the first half of the season and then acccepted to play on loan in Belarusian Premier League side Football Club Gomel the next half season.
The following seasons he played in Serbian second level sides FK Zemun and FK BSK Borča. During the winter-break of the 2014-2015 season he returns to Bosnia and signs with Premier League side FK Drina Zvornik.
Since then he played with another two Premier League clubs, FK Radnik Bijeljina and NK Vitez.