The 23-year-old Swiss driver joins race winner Stefano Coletti at the squad.
"I followed their races in the last few years and I'm sure I'll be able to take full advantage from some great support from them," said Trummer.
"Being able to run a second season in GP2 is a chance that some drivers don't get and I hope to reward the staff which support me with the best possible results."
Trummer only finished 23rd in the standings in his GP2 rookie season, but Rapax team boss Andrea Bergamini is confident he can make strong progress in 2013.
"Last year, making his debut in a tough series for rookies like GP2, he showed he is a consistent driver and adopted a really professional approach," Bergamini said.
"We hope to contribute to his growth and we admit we're looking forward to guiding him to his maiden top-notch results in the championship."