It is not clear what this question is about, but it appears to be an immigration question so I am moving it to that category. An application for immigration can be filed, but whether or not this old case will prevent the application from being successful will be determined by the facts of the case and by the quality of your legal representation. Hope this perspective helps!
The immigration consequences of convictions depend on the exact language of the statute under which the conviction took place.
You need to retain an experienced immigration lawyer to review all the facts, including the court disposition and the charging documents, in order to advise you, and handle the case.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.