Marks appeared in 14 games for New Orleans last season. He will back up Marcus Camby at center for Portland.
The native of New Zealand has averaged 3.0 points and 2.3 rebounds over his career.
The signing comes after center Fabricio Oberto retired last week because of palpitations connected to a cardiac condition.
Przybilla and Oden both had knee surgery last season. Przybilla is expected to return around Thanksgiving.