Goa Governor B V Wanchoo administered her oath of office at Raj Bhavan in the presence of Chief Minister Manohar Parrikar and others.
The by-election was necessitated by Matanhy Saldanha's death in March.
Alina won the by-election on a BJP ticket after Raymond D'Sa (Congress) and Ramakant Borkar (independent) withdrew from the fray.
Parrikar said he would announce on Monday the portfolios to be given to Alina. "I will consult her before deciding," he said.