The article: The Impact of Shoplifting Charges on Immigration Status
Some of the important points:
Theft is a crime of "moral turpitude":
Under federal immigration laws, theft crimes are considered crimes of moral turpitude. If a visa holder is convicted of a crime of moral turpitude, he or she may be deported from the country. A crime of moral turpitude is one that shocks the public conscious or is in contrast to community standards of justice, honesty and good morals.
Even permanent residents (green card holders):
It is not only nonimmigrant visa holders who need to be aware of the impact of being convicted of a crime on their immigration status. Those who hold valid legal resident status (green card) can also face removal proceedings for violating federal and state laws. Permanent residents who are convicted of an aggravated felony may be removed permanently from the country, no matter how long they have resided in the US or if they have family living here.
Additionally, shoplifting charges can stop citizenship proceedings.
Legal residents who want to become naturalized US citizens may find their path temporarily or even permanently blocked if they do not have a clean record.