Under the revised constitution, the body would have two vice presidents instead of its current eight.
Voting opens Wednesday and carries on until Friday.
The resolution passed with just one more vote than it needed.
Students who are on F-1 visas can't work more than 20 hours per week when school is in session.
Diversity VP Georgina Dodge promised last semester to create an advisory board for the center, but hasn't yet.
Zachary Schlaich, a senior computer engineering major, joined the RHA as a sophomore.
The vice president has made changes to the Nyumburu Cultural Center, a hub of black student life.
She will start in January.
The body rejected the amendment in its 11-hour end of session meeting.
Both the president and vice president positions were uncontested in the last three elections.