You can legally have a trespassing sign that says that trespassers will be shot but you cannot legally shoot at someone or shoot someone and injure the person or kill the person just because they're trespassing on your property.
The most you could do is point a shotgun at them if they don't leave the property but unless they're actually a threat to your life or your family then no you cannot shoot them for trespassing.
If someone is trespassing and they do not leave the property then you need to call the cops and have them removed from the property.
The trespasser will normally be given a warning first and then if they trespass again on the property and you call the cops then they'll be arrested.