Jacob Kramer was born into a Jewish family in Klintsy, Russia (now Klincy, Ukraine) on 26 December 1892, immigrating to England with his family and settling in Leeds in 1900. He studied at Leeds School of Art from 1907-1911, holding a senior scholarship in his final year. From 1913 he corresponded with Michael Sadler, modernist collector and Vice Chancellor of Leeds University, also attending Leeds Art Club. In the same year, he was awarded a Jewish Education Aid Society scholarship to study for one year at the Slade School of Fine Art in London, where his circle included ‘Whitechapel Boys’ Mark Gertler and David Bomberg. Bomberg and Jacob Epstein included his work as part of the so-called ‘Jewish Section’ in a review of modern movements at the Whitechapel Art Gallery in 1914 and he exhibited with the New English Art Club the same year. In 1915 he was elected a member of the London Group and included in the Vorticist exhibition at the Doré Galleries, London; he held his first solo exhibition in Bradford the same year. In 1916 he had a solo exhibition at Bradford Arts Club and in 1917 joined the Allied Artists Association, also lecturing at Leeds Art Club the same year. During the First World War he spent a short time as a regimental librarian, a post facilitated by Herbert Read. In 1919 he held a solo exhibition at Frank Rutter's Adelphi Gallery in London, returning to Leeds in 1920, where in 1931 he set up the Yorkshire Luncheon Group.

In 1935 Kramer had a solo exhibition at the Leger Galleries, London and participated regularly in Ben Uri's Annual Exhibition of Works by Jewish Artists from 1935–50. In 1960 Kramer's retrospective at the Leeds City Art Gallery attracted a record attendance. He died in the Jewish Home of Rest, Balham, London on 4 February 1962 and was buried in the Jewish cemetery at Gildersome in Leeds. Two posthumous exhibitions have been held at Ben Uri Gallery: Jacob Kramer Reassessed in 1984 (touring to Leeds, Bournemouth and Kingston-upon-Hull), and William Roberts & Jacob Kramer: The Tortoise and the Hare (touring to Leeds) in 2003. A Centenary exhibition was held at the University Gallery, Leeds in 1992.