Link joined the CDU in 1957 and was a member of the Frankfurt city council for the CDU from 1960 to 1969. In the 1969 federal elections Link was elected to the German Bundestag via the Hessian state list of the CDU. Link remained a member of the German Bundestag until 1990 and was initially always elected via the Hessian state list. In 1983 and 1987 he was elected directly in the Bundestag election district Frankfurt am Main III.
Herbst, Ludolf; Jahn, Bruno (2002). Vierhaus, Rudolf (ed.). Biographisches Handbuch der Mitglieder des Deutschen Bundestages. 1949–2002 [Biographical Handbook of the Members of the German Bundestag. 1949–2002] (in German). München: De Gruyter - De Gruyter Saur. p. 1715. ISBN978-3-11-184511-1.
Speaker: Marieluise Beck-Oberdorf, Petra Kelly, Otto Schily until 3 April 1984; Annemarie Borgmann, Waltraud Schoppe, Antje Vollmer until 30./31. January 1985;
Sabine Bard, Hannegret Hönes, Christian Schmidt until 1 February 1986; Annemarie Borgmann, Hannegret Hönes, Ludger Volmer until 18 July 1986); Willi Hoss (8 September 1986)
Speaker: Thomas Ebermann, Bärbel Rust, Waltraud Schoppe until 26 January 1988; Helmut Lippelt, Regula Schmidt-Bott, Christa Vennegerts until 30 January 1989, Helmut Lippelt, Jutta Oesterle-Schwerin, Antje Vollmer until 15 January 1990; Willi Hoss, Waltraud Schoppe (until 21 June 1990), Marianne Birthler (from 4 October 1990), Antje Vollmer