Wrinch was born at Rosario in Argentina and educated at Cambridge University, where she held a research fellowship from 1920 to 1924. She then taught physics at Oxford until 1939, when she moved to America to take up an appointment as lecturer in chemistry at Johns Hopkins University. In 1942 she moved to Smith College, remaining there until her retirement in 1959.

In 1934 Wrinch tackled the important problem of identifying the chemical carriers of genetic information. In common with other scientists at that time, she argued that chromosomes consisted of sequences of amino acids; these were the only molecules thought to possess sufficient variety to permit the construction of complex molecules. She proposed a model of the gene in the form of a T-like structure with a nucleic-acid stem and a sequence of amino acids as the cross bar.

In actual fact there were many such models in the 1930s. If it was not accepted that genes were made from specific sequences of amino acids then it became very difficult to see what they could come from. The trouble with all these models was that the experimentalists quickly found serious defects in them. Thus W. Schmidt in 1936 was able to show that Wrinch's model was incompatible with the known optical properties of nucleic acid and the chromosomes. The first suggestion that there might be an alternative to the protein structure of the gene came with the famous experiment of Oswald Avery in 1944.