Can a field be an entity?

Of course! Why not then? A field is something that exists on it's own, by itself. And it need not be material, but a field is in fact material.

But due to the fact you may be referring to a computer field on a website or program, yes that can also be considered an entity. Think of it as the fact that it is displayed on your monitor screen and is being projected from a computer, makes it exist nonetheless.