Yes. However, unless your spouse enters the U.S. on his/her own J-1 visa, they must enter the US as a J-2, dependent of the J-1 Exchange Visitor.

Once in the US the J-2 dependent can apply to the Department of Homeland Security–Bureau of Citizenship and Immigration Services (BCIS) for an Employment Authorization Document (EAD). The EAD must be obtained before work can begin. EAD processing times vary but generally take less than 120 days. A J-2 EAD is issued for the purpose of supporting the dependent only.