An Anglicism is a word or construction borrowed from English into another language.
Or, more prosaically (and more common), English loan.
OP asks for a counterpart to Sino-, which as @boiko points out, is Anglo-. But as a prefix in Sino-Korean and Sino-Japanese, Sino- has a connotation of hybridisation, or at least deeply enmeshed bilingualism (Sino-Korean = Chinese as spoken in Korea, Sinicised Korean). The counterpart to that with Anglo- is, if anything, Anglo-Norman: Norman French as spoken in England (and itself a source of loans into English).
Anglo-Korean would not work: it implies routine codeswitching and bilingualism. The connotation is much too strong for the present-day loans from English into Korean, which does not involve the same level of influence as Sino-Korean.