When did the term sci-fi come into usage?
According to ngrams it started increasing in popularity around 1965.
The OED online has a citation from 1954:
1954 Variety 17 Feb. 38/4 ‘Junior Science’, aside from its positive qualities, is a rewarding change of pace from the more thunderous sci-fi and spaceship packages.
And it notes that sci-fic and S.F. are earlier:
1929 Sci. Wonder Stories June 92/3 The S.F. Magazine. (Science-Fiction).
1948 G. Conklin Treas. Sci. Fiction p. ix, Many SF writers are feeling the urgent need for social controls over our physical powers.
1939 Le Zombie 18 Nov. 2 Popular Pubs does not now publish a sci-fic mag.
1952 J. Merril in Thrilling Wonder Stories Dec. 6/1 Does your science-fiction story taste different lately? Is the flat familiar stale taste disappearing?.. There's a reason. Its name is Synthesis, and sci-fic is its prophet.