Hossack, who was a secretary on the Interfraternity Council in 2013, was expelled from the university and Alpha Gamma Rho, OSU said.
The fraternity was placed on partial probation, according to OSU.
Alpha Gamma Rho President Mitchell Earl released a statement saying the fraternity did not condone or encourage Hossack's actions.
“Members of the fraternity are cooperating fully with campus officials and have no further comment due to the ongoing nature of the investigation,” Earl said.
Hossack's bail was set at $10,000, which he paid Monday, Payne County Jail officials said.
Both counts are felony charges and are punishable by imprisonment for one to 10 years, according to court documents.
His preliminary hearing is set for 10 a.m. Nov. 4.