Do I need to wait until my probation for D.U.I. is over to apply for green card (through marriage)?

A single DUI conviction will not stand in the way of eligibility to become a Permanent Resident, and a foreign national need not have completed probation in order to apply for Permanent Resident status. You may expect the USCIS to require, however, that probation be completed and that you supply certified copies of all disposition documents (including certified copies of records showing that you satisfied probation and the case is "closed") before an application for Permanent Resident status is approved. Note: sometimes it may be possible for a criminal defense attorney to ask the court to shorten a probation period, especially when there are important immigration-related considerations. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.