Aničić started his professional career at Zrinjski Mostar, before joining Astana in 2014.
[5] He won his first trophy with the club on 9 November, when they were crowned league champions for the first time in their history.
[6] Aničić helped Astana make their first historical UEFA Champions League appearance in 2015–16 season.
[16] In January 2021, he suffered a severe knee injury, which was diagnosed as anterior cruciate ligament tear and was ruled out for at least six months.
[19] In August 2015, he received his first senior call-up, for UEFA Euro 2016 qualifiers against Belgium and Andorra,[20] but had to wait until 25 March 2016 to make his debut in a friendly game against Luxembourg.