The Socialist Register is a socialist journal published annually. It was founded in 1964 by Ralph Miliband and John Saville. They had criticisms of the New Left Review after Perry Anderson became editor of the NLR in 1962. Miliband and Saville sought to bring about a journal in the orientation of The New Reasoner.
The current publisher of the Socialist Register is the Monthly Review Press. The journal's name is presumably a reference to the Social Register, a directory of American elites.
Its editors include Leo Panitch, Vivek Chibber and others.
References
Socialist Register Wikipedia(Text) CC BY-SA