An immigrant convicted of theft is deportable if the theft is considered an aggravated felony. These immigrants include any noncitizen of the U.S (valid visa holders and green card holders). For a case with an undocumented immigrant with no lawful status that’s convicted of theft, that alone can be the basis of deportation, not act of theft itself.
Immigration law contains a list of crimes which make an immigrant subject to deportation due to moral turpitude, and although theft is not included separately, it is included in the list of crimes that are considered aggravated felonies. Complications arise when the realization of theft, most often prosecuted under state law, are being judged using Federal statutes to determine severity. The result is that a crime of theft that may be considered a misdemeanor in the state court where it is prosecuted could be considered, and in some cases, to be an aggravated felony for federal immigration purposes. This is due to the varying standards applied by immigration law.
The benchmark for considering a crime of theft an aggravated felony is that the convictions of theft, receipt of stolen property, or burglary could have a sentence of at least one year. Immigration law can be complex when considering the interaction of state and federal statutes and it is often difficult to state any rule with certainty. A crime that is less serious in other contexts, such as a minor theft, could be elevated to an aggravated felony in the eyes of the immigration authorities and result in deportation.