Is stalking considered a crime of moral turpitude?
It most likely is, though the facts are important. Generally, a crime of moral turpitude is one that is seen as particularly immoral or contrary to society's values. Many crimes of assault, rape, murder, etc., to use major crimes as examples, would be crimes of moral turpitude, whereas shoplifting or auto theft often is not.
If the stalking was intended to terrify or harass the victim, or was motivated by "purient" interests (e.g. a sexual obsession with the victim), it would most likely be a crime of moral turpitude. On the other hand, one could imagine less common reasons for stalking that would not be: e.g., if you believe that the victim embezzled money from your company or business and are stalking them to try to get evidence that they are making major purchases or spending outrageous sums on leisure activity.