If you were put on probation and made to pay restitution, that would be considered guilty for immigration purposes, unless it was a pre-trial probation with the restitution being a civil repayment.
It is probably safe to renew your green card because the criminal checks aren't as thorough as with applying for citizenship, and most misdemeanors aren't deportable offenses. And you probably don't have much of a choice but to go ahead and try to renew, because failing to renew your card will cause you other problems in life anyway. But you shouldn't rely on anonymous message boards for something so serious. If you are concerned about it you should see an immigration attorney with expertise in criminal issues for a one-time consultation regarding the specific details of your offense (get the court records to show the attorney). Whether it is deportable depends on the amount involved, the circumstances, the jurisdiction, the specific classification of the theft, etc. which is not something you should expect us to answer.