If I was arrested for shoplifting 15 years ago, will it affect my green card application?

If this is your only criminal charge, it should not affect your green card application. However, you will need to admit to the charge on your application and the interviewing officer will need to see the docket sheet or other documents pertaining to the conviction.

One simple shoplifting arrest should not affect your eligibility for residency. However, expect that you will be questioned about it and that you will have to provide the court documents, etc. You may want to consult your case with an attorney, just to be safe.

Any incident of an arrest or criminal prosecution leading to a conviction is always of interest to DHS and your shoplifting arrest 15 years ago will come up during your status interview. If this is your only brush with the law, you should be eligible for a 601 waiver. You need to prove rehabilitation and that your admission will not be contrary to US interests I will still advise you to speak to an experienced attorney regarding the particulars of this arrest.