Hamburg recruit Rajkovic from Chelsea
Hamburg have made a poor start to the season and have taken just one point from three league games, conceding 10 goals. They were thrashed 5-0 by Bayern Munich on Saturday.
Serbia international Rajkovic, 22, joined Chelsea in 2007 but did not make a first-team start. He spent time on loan at PSV Eindhoven, Twente Enschede and Vitesse Arnhem.
"He is tall and an uncomfortable opponent who can scare other players," Hamburg coach Michael Oenning said of Rajkovic.
"He is bringing a quality we do not have and we need right now. On top of that he is left footed."
Oenning said Rajkovic could make his debut on Saturday in their league match against Cologne.