A cotton cultivar, designated DP 113 B2RF, is disclosed. The invention relates to the seeds of cotton cultivar DP 113 B2RF, to the plants of cotton DP 113 B2RF and to methods for producing a cotton plant produced by crossing the cultivar DP 113 B2RF with itself or another cotton variety. The invention further relates to hybrid cotton seeds and plants produced by crossing the cultivar DP 113 B2RF with another cotton cultivar.