AA is not a strictly Christian program, but you should feel that it is compatible with your religion.
"Alcoholics Anonymous is a fellowship of men and women who share their experience, strength, and hope with each other, that they may solve their common problem and help others to recover from alcoholism. The only requirement for membership is a desire to stop drinking. There are no dues or fees for AA membership. We are self supporting through our own contributions. AA is not allied with any sect, denomination, politics, organization, or institution; does not wish to engage in any controversy; neither endorses nor opposes any causes. Our primary purpose is to stay sober and help other alcoholics achieve sobriety."