Can my brother-in-law sponsor me to become a legal permanent resident?

Under family-based immigration, in-law relationships are not bases to approve immigrant visa petitions. No, your brother-in-law cannot file an immigrant visa petition for you if that is your only relationship with him. There are many ways to become a legal permanent resident. You can review your facts with an attorney to see if you have any bases to apply for visas that eventually may lead to LPR. You can review the information at www.uscis.gov for general information to immigration. If you have linguistic skills or medical skills, the US Armed Forces are starting a new program to recruit aliens without LPR status. If accepted, the aliens can apply for citizenship after a period of service.