
Eloğlu moved from Istanbul to Cologne as a four year old. The name "Şiir" is derived from her father, Metin Eloğlu (1927–1985), a painter and lyricist, who was awarded with important literature awards in the 1960s and 1970s.
After graduating from high school in Cologne, Eloğlu studied for four years at the Hochschule für Musik Saar in Saarbrücken. Her first engagements then took her to theatres in Erlangen, Oberhausen, and Cologne.
In 1991, she made her first film with Kinofilm, Happy Birthday, Türke!, directed by Doris Dörrie and acted with Ulrike Folkerts in her first scene. Eloğlu became known to a wider audience between 1993 and 1996 by her role of young assistant doctor Dr. Nesrin Ergün in the RTL series Stadtklinik.
At the end of 1997, she moved to Berlin. She followed TV and cinema productions as well as theater engagements, among others at the Düsseldorfer Schauspielhaus, where she acted in Antigone and Seven Against Thebes.
Her first international film production was the Swiss film 180° – Wenn deine Welt plötzlich Kopf steht, which was filmed by director Cihan Inan in Zürich. The international cast included Sophie Rois, Christopher Buchholz, Sabine Timoteo, and Michael Neuenschwander. The film ran at festivals in Antalya, Saarbrücken, Sudbury, and Marrakesh, as well as in the Spanish Ourense, where it received an award for Best Screenplay.
She was featured in Almanya - Welcome to Germany, directed by Yasemin Şamdereli, as Leyla Yılmaz. The film was awarded the Deutscher Filmpreis.
From 2014 to 2015, she played the architect Suna Kaya in the soap opera Lindenstraße.

Yellow Letters
2026 · as Rector

In the Fade
2017 · as Frau Sebnem

Tehran Taboo
2017 · as Schwiegermutter

Five Years
2013 · as Murat Kurnaz’ Mutter

Der Verdacht
2011 · as Putzfrau

Almanya: Welcome to Germany
2011 · as Leyla

Marco W. - 247 Tage im türkischen Gefängnis
2011 · as Richterin

A Spicy Kraut
2014 · as Emine Coscun

Servus, Schwiegersohn!
2019 · as Farah

Nachspielzeit
2015 · as Nurhan Ecevit

Tour Abroad
2000 · as Agent

Zone Rouge
2018 · as Semiha

180°
2010 · as Ülker Özel

Happy Birthday, Türke!
1992 · as Ayse

Die Schimmelreiter
2009 · as Arzu

Goster
2016 · as Ayse Nasreddin

Kückückskind
2014 · as Hatice Güngör

Matze, Kebab und Sauerkraut
2020 · as Melek Abu Yazid