A novel cotton cultivar, designated PM 2266 RR, is disclosed. The invention relates to the seeds of cotton cultivar PM 2266 RR, to the plants of cotton PM 2266 RR and to methods for producing a cotton plant produced by crossing the cultivar PM 2266 RR with itself or another cotton variety. The invention further relates to hybrid cotton seeds and plants produced by crossing the cultivar PM 2266 RR with another cotton cultivar.