Up to now, America has continued suppressing things by force, calling itself the world's policeman.
Literal
Until-now America [topic-は] world [gen-の] police [quotative-と] calling-itself, armed-force [to-に] relying suppression [obj-を] has-continued.
A political commentary sentence. 世界の警察と称して uses と (quotative) + 称する ('to call itself, to style itself') + て-form for 'calling itself X, doing Y.' 武力に頼る ('to rely on armed force') is a set collocation. 鎮圧 ('suppression, pacification') is a formal Sino-Japanese compound. 続けてきました is 続ける + ~てくる ('has continued up to the present') + polite past. The sentence exemplifies the measured, semi-formal register of Japanese political discourse.