Yes.  Many people become permanent residents (get a green card) through family members. The United States promotes family unity and allows U.S. citizens and permanent residents to petition for certain relatives to come and live permanently in the United States. You may be eligible to get a green card through a family member who is a U.S. citizen or permanent resident, or through a different avenue. 

There are two distinct paths through which you can get your green card. Many family members who are already in the United States may qualify for adjustment of status to permanent residence in the United States, which means they are able to complete their immigrant processing without having to return to their home country. Those relatives outside the United States or those who are not eligible to adjust status in the United States may be eligible for consular processing through a U.S. embassy or consulate abroad that has jurisdiction over their foreign place of residence.