You can get married and amend your asylum application to include her. A pending asylum application does not grant legal status but permits the applicant to remain in the U.S. while the asylum application is pending. However, while the asylum application is pending she may be eligible to apply for an Employment Authorization Card (EAD) and if approved she will gain permission to work in the U.S. If your asylum application is granted you can file for a green card and adjust to a Lawful Permanent Resident (LPR) one year after the grant of asylum. Your spouse will receive a derivative grant of asylum through your application if approved and can also file for a green card one year after the grant of asylum.

Please be advised that there are special considerations in each case and it is best to consult with an experienced immigration attorney.