Rossbach started his career with local clubs Stridklev, Urædd and Pors Grenland. In 1986 when Ham-Kam was promoted to the Norwegian Premier League they signed Rossbach. In 1990 Rossbach moved to Tromsø, and became part of the Tromsø team who finished second in the top flight. After a year in Tromsø Rossbach moved to Oslo to play for Lyn and to attend the Norwegian Police University College. Rossbach have made comebacks for both Tollnes and Pors Grenland when the clubs struggeled with injuries on their goalies, the last time in 2004, when he at the age of 39, guarded the goal in the first games of the season. He's currently working at Grenland police station.