Your half sister is still your sister, there is no discrimination for half siblings, so yes, you can petition for her if all the other requirements are met. The fact that your mother died when you were little does not change anything. However, waiting times for siblings are very long, so you should be patient to reunite with your sister.
No problem. You can apply for her, though it will take many years.
Samuel Ouya Maina, Esq. 415.391.6612 email@example.com Law Offices of S. Ouya Maina, PC 332 Pine Street, Suite 707 San Francisco, CA 94104
The laws of immigration consider a half sister your sister but you can only petition her if you are a United States Citizen. That opportunity isn't available for US green card holders.