I moved you to immigration because this is an immigration question, not a criminal defense question.
Impossible to provide you with a definitive answer, particularly on this forum. It will depend on your criminal record as well as other factors. In this climate, it is really advisable to consult with an experienced immigration attorney if you have any sort of criminal record, no matter how minor.
This answer provides general information only. Please see an experienced immigration attorney for a complete answer. 203 645 6376.
There is not enough information in your question to give you a meaningful answer. While the fact that it was 19 years ago is in your favor, any criminal problem can possibly cause headaches for you.
My strongest suggestion would be that you consult with an experienced immigration attorney in your area for expert assistance.
This answer is of a general nature and should not be relied upon as final, nor is it intended as legal advice. A consultation with an experienced attorney is always the best way to go.
Sorry, I do not do immigration law, but you should immediately contact one to help you out. I am hoping that if your record has been clear in the last 19 years that this misdemeanor theft will not hurt your chances. But, see an immigration lawyer for advice.
Although I am an experienced CA criminal defense and appeals attorney, I can not 'guarantee' that my answer is entirely accurate, since I have not reviewed all of the factual circumstances of the case, nor have I discussed those circumstances fully with the questioner. The fact that I have answered this question does not establish an attorney client relationship between the questioner and my self or my office.
I agree with my colleagues that you would need a review of your criminal history and other immigration history to determine for certain whether there could be a problem with an application for citizenship. There are a couple positive factors you mention, including that the conviction is old and that your sentence was less than one year. However, it certainly would be best to consult with a licensed, experienced immigration attorney (and not an unlicensed notary or consultant, of which we have many here in the Central Valley, so please do be very cautious) to determine whether and how the conviction could affect you.
Ms. Doerrie's answer to your question is general in nature, as not all facts and circumstances relating to the specific person(s) and situations involved are known to her. Ms. Doerrie recommends consulting with an immigration attorney regarding your specific facts and circumstances prior to making any legal decision or submitting any form or application. This response does not create an attorney/client relationship.