Is it a bad practice to add elements to List using getter method in java?

I would suggest in this case it would be best to follow your Encapsulation principals and use a method for adding elements to the list. You have restricted access to your list by making it private so that other classes cannot directly access the datatype.

Let the class that stores your ArrayList have direct access to the list, but when other classes want to add to the list, use an add() method.

I don't think it a particularly great practice to do something like:

myObj.getMyList().add(x);

since you are exposing a private class variable in a non read only way, but that being said I do see it pretty frequently(I'm looking at you, auto generated classes). I would argue that instead of doing it that way, return an unmodifiable list and allow users of the class to add to the list via an explicit method:

public class MyClass{
    private final List<String> myList = new ArrayList<String>();

    public List<String> getList(){
        return Collections.unmodifiableList(this.myList);
    }

    public void addToList(final String s){
        this.myList.add(s);
    }
}

EDIT After reviewing your comments, I wanted to add a bit about your setter idea:

I meant using that line of code inside a new kind of setter inside the class itself, like public void setter(someElement){this.myLinkedList.add(someElement);}

If I'm understanding you correctly, you are saying you want to expose a method that only adds to your list. Overall this is what I think you should be shooting for, and what many have outlined in the answers, however, labeling it as a setter is a bit misleading since you are not reassigning (setting) anything. That, and I strongly recommend returning a read only list from your getter method if possible.