The house is for two members of the fraternity's housekeeping staff - Lion and Zar Ree Wei, and their six children.
Smith, 20, of Houston, Texas, died on August 23 along Interstate 85 in Randolph County when police shot him shortly after he called 911 to report he was armed with a 9mm pistol and was feeling suicidal.
Investigators later ruled that officers had reason to believe Smith was armed and made a threatening gesture, and therefore the shooting was justified.
Incoming DKE president Davis Willingham said the Habitat house is a way for the fraternity chapter to deal with the enormous loss.
"His big heart and vibrant personality touched us and we feel this is a significant effort to honor his life, selfless nature, and affinity for service. Building the house will benefit the Wei family and ensure Courtland’s legacy as an exemplary leader,” said Willingham in a news release.