Having a criminal conviction could affect your immigration status, but not every crime will result in deportation. It depends on the type of crime.
FindLaw explains that deportation for a criminal conviction typically occurs only for crimes involving moral turpitude or aggravated felonies. If your conviction does not fall into these categories, then you probably will not have to concern yourself with deportation unless you commit crimes that the law specifically states will result in deportation, such as human trafficking, child abuse, stalking and domestic violence.
Crimes of moral turpitude are difficult to define because immigration officials do not clearly define it. Because of this, many criminal convictions could fit into this category. However, courts have made rulings to help narrow down what crimes should be crimes of moral turpitude.
In general, crimes that fall into this category include anything that breaches trust and involves dishonesty. For example, assault, perjury and fraud all fit into this category. However, there is a long list of crimes that can fit into this category that may not seem obvious at first.
Aggravated felonies are crimes the Immigration and Nationality Act specifically designate. These include any violent crime with a possible sentence of at least one year in prison, drug trafficking, murder, rape, firearm offenses and theft.
You should note that even though the INA lists these as felonies, you could face deportation for a misdemeanor that falls into this category. The INA does not account for how the criminal law defines or categorized the offense. If it is on the list, then it is a deportable offense even if it was a misdemeanor charge.