A novel soybean cultivar, designated SG1120RR, is disclosed. The invention relates to the seeds of soybean cultivar SG1120RR, to the plants of soybean SG1120RR and to methods for producing a soybean plant produced by crossing the cultivar SG1120RR with itself or another soybean variety. The invention further relates to hybrid soybean seeds and plants produced by crossing the cultivar SG1120RR with another soybean cultivar.