Anghelini, who is of Italian descent, played for hometown club Steagul Roșu Brașov between 1971 and 1974, before joining Steaua București, where he spent 10 seasons, winning two league titles and two Romanian Cups.

[1][3][4][5][6][7] He made his Divizia A debut on 3 May 1972, aged 18 under the guidance of coach Nicolae Proca in a 2–0 away loss in front of UTA Arad.

[1][8][9] In the following season he reached another Cupa României final, Jenei using him all the minutes in the eventual 2–1 loss in front of Universitatea Craiova.

[1][8] In next two seasons, under the guidance of coach Gheorghe Constantin he reached two more Cupa României finals, playing all the minutes in both, the first one ending with a 3–0 win over Sportul Studențesc București and the one from 1980 with a 2–1 loss in front of Politehnica Timișoara.

[1] Teodor Anghelini played 22 matches at international level for Romania, making his debut under coach Valentin Stănescu on 23 March 1974 in a friendly which ended with a 1–0 loss in front of France.