Rašić was born on 27 January 1973 in Dobrotin, a village near Lipljan, in the SAP Kosovo, SR Serbia, SFR Yugoslavia.

[2] Following the end of hostilities in Kosovo, Rašić worked as a translator for British KFOR troops and later for the International Organization for Migration.

On 9 January 2008, Rašić was appointed minister of labor and social welfare of Kosovo as part of the cabinet of Hashim Thaçi and served in this position until 2014.

Mirić's party left the alliance because of an election campaign video that Rašić recorded in Albanian language.

[11] On 23 April, Rašić resigned because of the indictment brought against him for alleged abuse of official duty[12] and was succeeded by Cvetko Veljković.

[14] Rašić endorsed the Civic Initiative for Freedom, Justice and Survival (GI SPO) for the 2021 parliamentary elections as he was unable to run as candidate due to the indictment against him.

[18] On 1 December 2022, Rašić was appointed minister for communities and returns by Albin Kurti after the post was left vacant for almost one month following the resignation of Goran Rakić and the Serb List's (SL) boycott of Kosovan institutions.

[21] SL reacted with a statement that Rašić's appointment was unconstitutional as it wasn't approved by Serb MP's and announced that it will submit an appeal to the Constitutional Court of Kosovo.

[28] In the 2025 parliamentary election campaign, the Serb Democracy (SD) and its leader Aleksandar Arsenijević accused SPO of vote buying.