The deal is valued at $1.1bn (Â£780m).
The Carmike acquisition comes on the heels of Wanda buying studio Legendary Entertainment, the company behind blockbusters like Jurassic World and The Dark Knight.
Dalian Wanda, the world's biggest movie theatre operator, took over AMC in 2012 for $2.6bn.
The rapidly growing company is led by China's richest man, Wang Jianlin.
Mr Wang has been looking to buy a Hollywood studio for several years and was reported to be in talks with DreamWorks Animation last year, but a deal was not announced.
AMC Entertainment currently has 387 locations and 5,426 screens while Carmike has 276 theatres with 2,954 screens.
AMC Entertainment, a US cinema chain owned by Chinese conglomerate Dalian Wanda, is acquiring rival Carmike, creating the largest US cinema chain.