Agang wants secret no-confidence ballot
The party approached the Constitutional Court in Johannesburg to decide on the matter.
The party first tabled the motion in the National Assembly in early November.
It also wants Speaker of Parliament Baleka Mbete to be declared unfit to hold office.
"It's no use bickering in Parliament about one issue after the other, while the issue clearly is the head of state. Agang is of the opinion that Zuma needs to be removed [from office] in order for us to be put back on the path of restoration," the party's Aubrey Plaatjies said.
The start-up political party wants the motion debated soon after the 2015 State of the Nation Address.
African National Congress (ANC) and opposition Members of Parliament (MPs) in 2012 clashed over whether a motion of no-confidence in the president could be debated before the ruling party's crucial elective conference in Mangaung.
AgangSA says MPs should be able to vote without fear of persecution.
In an unprecedented move two years ago, several opposition parties tried to have a motion of no-confidence in the president debated but the ruling party blocked attempts to schedule the debate.
But the country's top court essentially sent political parties back to Parliament to work out the issues there.