Rašić began his professional career during the 2003–04 season with Borac Čačak. He then moved to FMP Zeleznik.
In March 2007, he signed with the Turkish team Efes Pilsen, where he stayed for the rest of the season.
In August 2007, he signed a two-year deal with the Russian team Dynamo Moscow. In November 2007 he was released by Dynamo.
In November 2007, he signed with the German team ALBA Berlin for the remainder of the season. With them he won the Bundesliga.
In July 2008, he returned to Serbia and signed with Partizan.
In September 2010, he signed with the Turkish team Trabzonspor. In March 2011, he moved to Lithuania and signed with Lietuvos rytas until the end of the 2011–12 season.
In August 2012, he signed a one-year deal with the Italian powerhouse Montepaschi Siena. With them he won the Italian League and Cup.
In October 2013, he moved to Turkey and signed a one-year deal with TED Ankara Kolejliler. In July 2014, he signed with another Turkish team Torku Konyaspor.
On September 2, 2015, he signed with the Romanian club Steaua București. On December 12, 2015, he left Steaua and signed with the Turkish club Türk Telekom. On May 2, 2016, he signed with Mega Leks for the rest of the season.
On July 8, 2016, Rašić signed with Romanian club U BT Cluj-Napoca.
As a member of the senior men's Serbian national basketball team, Rašić played at the 2010 FIBA World Championship and the EuroBasket 2011.
Note: The EuroLeague is not the only competition in which the player participated for the team during the season. He also played in domestic competition, and regional competition if applicable.