Andrey Arshavin, 34, spent the first half of the 2015-16 season at Kuban Krasnodar, but left the club by mutual consent during Russia's winter break.
Former Russia international Arshavin, 34, joined Kuban in July but the deal was terminated six months early after making only nine appearances.
Sunjic, 26, replaces Germany international Antonio Rudiger, who was transferred to Roma earlier this month.
Andrey Arshavin joined Russian Premier League team Kuban Krasnodar on Monday after leaving Zenit St Petersburg.
Lokomotiv Moscow won the Russian Cup on Thursday, defeating Kuban Krasnodar 3-1 in extra time to lift its first trophy for eight years.
|Zenit St Petersburg||19||14||3||2||+28||45|
|FC Arsenal Tula||19||7||4||8||0||25|
|Ural Sverdlovsk Oblast||19||6||6||7||-7||24|
|FK Rubin Kazan||19||4||7||8||-10||19|