A novel cotton variety, designated as FM 960B2R, is disclosed. The invention relates to seeds, plants, plant cells, plant tissue, harvested products and cotton lint as well as to hybrid cotton plants and seeds obtained by crossing plants of variety FM 960B2R with other plants. The invention also relates to plants and varieties produced by the method of essential derivation from plants of FM 960B2R and to plants of FM 960B2R reproduced by vegetative methods, including but not limited to tissue culture of regenerable cells or tissue from FM 960B2R.